High resolution magnetic field sensors

ABSTRACT

A magnetic field sensor includes a plurality of magnetic field sensing elements configured to generate at least two measured magnetic field signals indicative of a magnetic field affected by an object and having a first predetermined phase difference with respect to each other and a controller responsive to the at least two measured magnetic field signals. The controller is configured to generate an angle signal and to compare the angle signal to at least one angle signal threshold. The angle signal can be compared to a plurality of angle signal thresholds to generate a plurality of output transitions, each output transitions indicative of the angle signal crossing the corresponding angle signal threshold. The number of angle signal thresholds can be dependent upon a desired number of output transitions per pole-pair of the angle signal.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a Continuation-in-Part (CIP) application and claimsthe benefit of and priority to U.S. patent application Ser. No.16/290,017, filed on Mar. 1, 2019, which application is incorporated byreference herein in its entirety, and which is a Continuation-in-Part(CIP) application of and claims the benefit of and priority to U.S.patent application Ser. No. 16/010,969, filed on Jun. 18, 2018, whichapplication is incorporated by reference herein in its entirety.

STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH

Not Applicable.

FIELD

This disclosure relates generally to magnetic field sensors and moreparticularly, to magnetic field sensors providing high resolutionoutputs.

BACKGROUND

As is known, sensors are used in various types of devices to measure andmonitor properties of systems in a wide variety of applications. Forexample, sensors have become common in products that rely on electronicsin their operation, such as automotive and motor control systems.

Some sensors monitor properties by detecting a magnetic field associatedwith proximity or movement of a target object with respect to one ormore magnetic field sensing elements. In magnetic field sensorsincluding multiple magnetic field sensing elements, magnetic fieldsignals from the sensing elements can be processed by separateprocessing channels to generate respective phase separated signals. Onesuch magnetic field sensor is the Allegro MicroSystems, LLC ATS605LSGDual Output Differential Speed and Direction Sensor IC, in which theoutput signal from each of the two processing channels is provided at arespective output pin of the sensor integrated circuit (IC). The channeloutput, or speed signals can be provided in the form of two-state binarysignals having a frequency indicative of the speed of rotation of thetarget object. Additional output signals can include a direction signalindicative of a direction of rotation of a target object and/or anexclusive OR (XOR) speed signal that provides a signal resulting from anXOR logic operation based on the speed signals.

There are applications for which it is desirable that a magnetic fieldsensor provide a higher resolution of angular detection of the targetobject than can be accomplished with two speed signals or the XOR speedsignal, for example to permit tighter control and better reactivity tochange in position. While angular resolution can be increased by usingadditional sensors in different physical locations and/or by using morecomplex targets, these solutions can require more physical size for thesensor installation, higher costs for more sensing components, and/ormore manufacturing complexity.

SUMMARY

According to the disclosure, a method includes generating first andsecond magnetic field signals having a predetermined phase differencewith respect to each other, the first and second magnetic field signalsindicative of a magnetic field affected by an object, generating anangle signal from the first and second magnetic field signals, the anglesignal indicative of an angle of the magnetic field, and comparing theangle signal to a at least one angle signal threshold to generate a atleast one output transition.

Features may include one or more of the following individually or incombination with other features. Generating the second magnetic fieldsignal may include generating a virtual magnetic field signal from thesecond magnetic field signal, wherein the virtual magnetic field signalhas a second predetermined phase difference with respect to the firstmagnetic field signal, and wherein the angle signal is generated fromthe first magnetic field signal and the virtual magnetic field signal.Generating the first and second magnetic field signals may includegenerating first and second virtual magnetic field signals fromrespective first and second measured magnetic field signals, the firstand second virtual magnetic field signals having a second predeterminedphase difference with respect to each other. The virtual magnetic fieldsignals may be generated according to a mathematical function thatcharacterizes a relationship between the second predetermined phasedifference and at least one of the two measured magnetic field signals.The predetermined phase difference may be 90 degrees. A direction ofrotation of the object may be determined based on a polarity of a slopeof the angle signal. The method may further include comparing the firstmagnetic field signal to a poscomp threshold to generate a first squarewave signal, and comparing the second magnetic field signal to theposcomp threshold to generate a second square wave signal, and wherein adirection of rotation of the object is determined by determining whetherthe first square wave signal leads or lags the second square wavesignal. The poscomp threshold can be predetermined or based on anamplitude of the first magnetic field signal and the second magneticfield signal. The method may further include comparing the angle signalto a plurality of angle signal thresholds to generate a correspondingplurality of output transitions, each output transition indicative ofthe angle signal crossing the corresponding angle signal threshold. Theplurality of angle signal thresholds can include at least fourthresholds. A number of angle signal thresholds of the plurality ofangle signal thresholds can be dependent upon a desired number of outputtransitions per pole-pair of the angle signal. The angle signalthresholds may be generated according to the equations:

${k = {\frac{N_{OC}}{2} - 1}},{N_{OC} = 2},4,6,{\ldots \mspace{14mu};{and}}$${{T\left( N_{OC} \right)} = {\left( \frac{\pi}{N_{OC}} \right) \cdot \left\{ {\tau_{0}\mspace{14mu} \ldots \mspace{14mu} \tau_{k}} \right\}}},{{\tau_{i} = {{2 \cdot i} - k}};}$

where τ is a threshold number, k is the total number of angle signalthresholds, N_(OC) is a desired number of output transitions, and T is avalue of the threshold number for each threshold.

The angle signal can be calculated according to a mathematical functionthat integrates a time derivative of the first and second magnetic fieldsignals. The mathematical function can include:

${y = {{\arctan \left( {f(t)} \right)} = {\int{\frac{f^{\prime}(t)}{1 + {f^{2}(t)}}{dt}}}}},$

where ƒ(t) is a function that is based on a ratio of the first andsecond magnetic field signals.

Also described is a magnetic field sensor including a plurality ofmagnetic field sensing elements configured to generate at least twomeasured magnetic field signals indicative of a magnetic field affectedby an object and having a predetermined phase difference with respect toeach other and a controller responsive to the at least two measuredmagnetic field signals and configured to generate an angle signal and tocompare the angle signal to at least one angle signal threshold and togenerate at least one output transition.

Features may include one or more of the following individually or incombination with other features. The phase difference may bepredetermined and, in some embodiments may be 90-degrees. The controllercan be further configured to determine a direction of rotation of theobject is based on a polarity of a slope of the angle signal. Thecontroller can be further configured to compare the first magnetic fieldsignal to a poscomp threshold to generate a first square wave signal,and compare the second magnetic field signal to the poscomp threshold togenerate a second square wave signal, and to determine a direction ofrotation of the object is by determining whether the first square wavesignal leads or lags the second square wave signal. The controller canbe configured to compare the angle signal to a plurality of angle signalthresholds and to generate a plurality of output transitions, eachoutput transition indicative of the angle signal crossing thecorresponding angle signal threshold. The plurality of thresholds caninclude at least four thresholds. A number of angle signal thresholds ofthe plurality of angle signal thresholds can be dependent upon a desirednumber of output transitions per pole-pair of the angle signal. Theangle signal thresholds can be generated according to the equations:

${k = {\frac{N_{OC}}{2} - 1}},{N_{OC} = 2},4,6,{\ldots \mspace{14mu};{and}}$${{T\left( N_{OC} \right)} = {\left( \frac{\pi}{N_{OC}} \right) \cdot \left\{ {\tau_{0}\mspace{14mu} \ldots \mspace{14mu} \tau_{k}} \right\}}},{{\tau_{i} = {{2 \cdot i} - k}};}$

where τ is a threshold number, k is a total number of angle signalthresholds, N_(OC) is a desired number of output transitions, and T is avalue of the threshold number for each threshold number. The anglesignal can be calculated according to a mathematical function thatintegrates a time derivative of the first and second magnetic fieldsignals. The mathematical function can include:

${y = {{\arctan \left( {f(t)} \right)} = {\int{\frac{f^{\prime}(t)}{1 + {f^{2}(t)}}{dt}}}}},$

where ƒ(t) is a function that is based on a ratio of the first andsecond magnetic field signals. The output transitions can be equidistantwith respect to each other. The output transitions can be equidistanteach period-on-period of the angle signal. The arctangent of the firstand second magnetic field signals can be determined without the sampletime of the angle signal. The plurality of magnetic field sensingelements can include one or more Hall effect elements and/ormagnetoresistance elements.

Also described is a magnetic field sensor including means for generatingfirst and second magnetic field signals having a predetermined phasedifference with respect to each other, the first and second magneticfield signals indicative of a magnetic field affected by an object,means for generating an angle signal from the first and second magneticfield signals, the angle signal indicative of an angle of the magneticfield, and means for comparing the angle signal to at least one anglesignal threshold to generate at least one output transition. The meansfor generating the first and second magnetic field signals can includemeans for generating first and second virtual magnetic field signalsfrom respective first and second measured magnetic field signals.

BRIEF DESCRIPTION OF THE DRAWINGS

The foregoing features of the disclosure, as well as the disclosureitself may be more fully understood from the following detaileddescription of the drawings. The drawings aid in explaining andunderstanding the disclosed technology. Since it is often impractical orimpossible to illustrate and describe every possible embodiment, theprovided figures depict one or more exemplary embodiments. Accordingly,the figures are not intended to limit the scope of the invention. Likenumbers in the figures denote like elements.

FIG. 1 shows a block diagram of a dual-channel magnetic field sensorusing an arbitrary number of thresholds to provide output transitionsrepresentative of a speed and/or a direction of rotation of an object,according to the present disclosure;

FIG. 2 shows a more detailed diagram of a dual-channel magnetic fieldsensor using an arbitrary number of thresholds, according to the presentdisclosure;

FIG. 3 shows a graph of example waveforms including input magnetic fieldsignals, normalized signals, an angle signal, and associated outputsignals according to the present disclosure as may be generated by anyof the sensors of FIG. 1-2 or 10-10C;

FIG. 4 is a flow diagram illustrating a method of generating at leastone output transition from an angle signal, according to the presentdisclosure;

FIG. 5 is a graph of example waveforms including input magnetic fieldsignals, an angle signal, and various associated output signalsgenerated by angle signal thresholds placed dependent upon a desirednumber of output commutations per pole-pair of the magnetic fieldsignals, according to the present disclosure as may be generated by anyof the sensors of FIG. 1, 2, or 10-10C;

FIG. 6 is a flow diagram illustrating a method of implementing anarctangent calculator according to the present disclosure;

FIG. 7 is a block diagram illustrating an arctangent calculation systemimplementing a forward Euler integrator, according to the presentdisclosure;

FIG. 8 is a block diagram illustrating an arctangent calculation systemimplementing a backward Euler integrator, according to the presentdisclosure;

FIG. 9 is a block diagram illustrating an arctangent calculation systemimplementing a trapezoidal integrator, according to the presentdisclosure;

FIG. 10 shows a voltage-level output magnetic field sensor according tothe disclosure;

FIG. 10A shows a current-level output magnetic field sensor according tothe disclosure;

FIG. 10B shows an alternative voltage-level output magnetic field sensoraccording to the disclosure;

FIG. 10C shows another alternative voltage-level output magnetic fieldsensor according to the disclosure;

FIG. 11 shows example waveforms, including measured magnetic fieldsignals, a virtual magnetic field signal, and associated channel outputsignals according to the disclosure as may be generated by any of thesensors of FIGS. 10-10C;

FIG. 12 is a simplified flow diagram illustrating a method of generatingone or more virtual magnetic field signals according to the disclosure;

FIG. 12A is a flow diagram illustrating a method of generating one ormore virtual magnetic field signals according to the disclosure;

FIG. 13 shows example waveforms, including measured magnetic fieldsignals, a plurality of virtual magnetic field signals, and associatedchannel output signals according to the disclosure as may be generatedby any of the sensors of FIGS. 10-10C;

FIG. 14 shows example waveforms of two measured magnetic field signalsand two virtual magnetic field signals, and the associated outputpulses, where there is no phase error between the first and secondchannels that generate the measured magnetic field signals;

FIG. 15 shows example waveforms of the output signal, wheeldisplacement, and wheel displacement error, where there is no phaseerror between the first and second channels that generate the measuredmagnetic field signals;

FIG. 16 shows example waveforms of two measured magnetic field signalsand two virtual magnetic field signals, and the associated outputpulses, where there is a 30-degree phase error between the first andsecond channels that generate the measured magnetic field signals;

FIG. 17 shows example waveforms of the output signal, wheeldisplacement, and wheel displacement error, where there is a 30-degreephase error between the first and second channels that generate themeasured magnetic field signals;

FIG. 18 is a diagram of an example virtual signal generator forgenerating virtual quadrature magnetic field signals, according to thedisclosure;

FIG. 19 shows example waveforms of measured magnetic field signals andtwo virtual quadrature magnetic field signals, according to thedisclosure;

FIG. 20 shows an example waveform for an amplitude correction curve usedin generating virtual quadrature magnetic field signals, according tothe disclosure;

FIG. 21 is a flow diagram illustrating a method of generating one ormore virtual quadrature magnetic field signals;

FIG. 22 is a diagram of an example virtual signal generator forgenerating virtual arbitrary magnetic field signals, according to thedisclosure; and

FIG. 23 is a flow diagram illustrating a method of generating one ormore virtual arbitrary magnetic field signals, according to thedisclosure.

DETAILED DESCRIPTION

Before describing the present invention, some introductory concepts andterminology are explained. As used herein, the term “rotation detector”is used to describe a circuit that includes at least one “magnetic fieldsensing element” which detects a magnetic field. The rotation detectorcan sense movement, e.g., rotation, of a ferromagnetic object, forexample, advance and retreat of magnetic domains of a ring magnet oradvance and retreat of gear teeth of a ferromagnetic gear. Similarly,the term “movement detector” can be used to describe either a rotationdetector or a magnetic field sensor that can sense different movement,e.g., linear movement, of a ferromagnetic object, for example, linearmovement of magnetic domains of a ring magnet or linear movement of gearteeth of a ferromagnetic gear.

As used herein, the term “magnetic field sensing element” is used todescribe a variety of electronic elements that can sense a magneticfield. The magnetic field sensing element can be, but is not limited to,a Hall effect element, a magnetoresistance element, or amagnetotransistor. As is known, there are different types of Hall effectelements, for example, a planar Hall element, a vertical Hall element,and a Circular Vertical Hall (CVH) element. As is also known, there aredifferent types of magnetoresistance elements, for example, asemiconductor magnetoresistance element such as Indium Antimonide(InSb), a giant magnetoresistance (GMR) element, for example, a spinvalve, an anisotropic magnetoresistance element (AMR), a tunnelingmagnetoresistance (TMR) element, and a magnetic tunnel junction (MTJ).The magnetic field sensing element may be a single element or,alternatively, may include two or more magnetic field sensing elementsarranged in various configurations, e.g., a half bridge or full(Wheatstone) bridge. Depending on the device type and other applicationrequirements, the magnetic field sensing element may be a device made ofa type IV semiconductor material such as Silicon (Si) or Germanium (Ge),or a type semiconductor material like Gallium-Arsenide (GaAs) or anIndium compound, e.g., Indium-Antimonide (InSb).

As is known, some of the above-described magnetic field sensing elementstend to have an axis of maximum sensitivity parallel to a substrate thatsupports the magnetic field sensing element, and others of theabove-described magnetic field sensing elements tend to have an axis ofmaximum sensitivity perpendicular to a substrate that supports themagnetic field sensing element. In particular, planar Hall elements tendto have axes of sensitivity perpendicular to a substrate, while metalbased or metallic magnetoresistance elements (e.g., GMR, TMR, AMR) andvertical Hall elements tend to have axes of sensitivity parallel to asubstrate.

As used herein, the term “magnetic field sensor” or simply “sensor” isused to describe a circuit that uses one or more magnetic field sensingelements, generally in combination with other circuits. The magneticfield sensor can be, for example, a rotation detector, a movementdetector, a current sensor, or a proximity detector.

Magnetic field sensors are used in a variety of applications, including,but not limited to an angle sensor that senses an angle of a directionof a magnetic field, a current sensor that senses a magnetic fieldgenerated by a current carried by a current-carrying conductor, amagnetic switch that senses the proximity of a ferromagnetic object, arotation detector (or movement detector) that senses passingferromagnetic articles, for example, magnetic domains of a ring magnetor a ferromagnetic target (e.g., gear teeth) where the magnetic fieldsensor is used in combination with a back-bias or other magnet, and amagnetic field sensor that senses a magnetic field density of a magneticfield.

As used herein, the terms “processor” and “controller” are used todescribe electronic circuitry that performs a function, an operation, ora sequence of operations. The function, operation, or sequence ofoperations can be hard coded into the electronic circuit or soft codedby way of instructions held in a memory device. The function, operation,or sequence of operations can be performed using digital values or usinganalog signals. In some embodiments, the processor or controller can beembodied in an application specific integrated circuit (ASIC), which canbe an analog ASIC or a digital ASIC, in a microprocessor with associatedprogram memory and/or in a discrete electronic circuit, which can beanalog or digital. A processor or controller can contain internalprocessors or modules that perform portions of the function, operation,or sequence of operations. Similarly, a module can contain internalprocessors or internal modules that perform portions of the function,operation, or sequence of operations of the module.

While electronic circuits shown in figures herein may be shown in theform of analog blocks or digital blocks, it will be understood that theanalog blocks can be replaced by digital blocks that perform the same orsimilar functions and the digital blocks can be replaced by analogblocks that perform the same or similar functions. Analog-to-digital ordigital-to-analog conversions may not be explicitly shown in the figuresbut should be understood.

It should be understood that a so-called “comparator” can be comprisedof an analog comparator having a two state output signal indicative ofan input signal being above or below a threshold level (or indicative ofone input signal being above or below another input signal). However,the comparator can also be comprised of a digital circuit having anoutput signal with at least two states indicative of an input signalbeing above or below a threshold level (or indicative of one inputsignal being above or below another input signal), respectively, or adigital value above or below a digital threshold value (or anotherdigital value), respectively.

As used herein, the term “predetermined,” when referring to a value orsignal, is used to refer to a value or signal that is set, or fixed, inthe factory at the time of manufacture, or by external means, e.g.,programming, thereafter. As used herein, the term “determined,” whenreferring to a value or signal, is used to refer to a value or signalthat is identified by a circuit during operation, after manufacture.

Ferromagnetic objects described herein can have a variety of forms,including, but not limited to a ring magnet having one or more pole pairor a gear having two or more gear teeth. Ferromagnetic gears are used insome examples below to show a rotating ferromagnetic object havingferromagnetic features, i.e., teeth. However, in other embodiments, thegear can be replaced with a ring magnet having at least one pole pair.Also, linear arrangements of ferromagnetic objects that move linearlyare possible.

FIG. 1 shows a block diagram of a dual-channel magnetic field sensor2000 using an arbitrary number of angle signal thresholds to provideoutput transitions representative of a speed and/or a direction ofrotation of an object, according to the present disclosure. The sensor2000 may be the same as or substantially similar to the sensor 10 shownin FIG. 10, sensor 10′ shown in FIG. 10A, sensor 100 shown in FIG. 10B,or sensor 170 shown in FIG. 10C, or may include some but not all of thecomponents of the sensor 10, 10′, 100, or 170, or may include additionalfeatures not shown in sensor 10, 10′, 100, or 170.

The sensor 2000 includes a first channel 2010 and a second channel 2020that provide respective outputs 2011, 2021 to an angle generation unit2030, which is coupled to a direction detection unit 2040 that providesa direction output 2042 and a high resolution “Hi Res” output 2044.

The first channel 2010 includes a first magnetic field sensing element2012 coupled to an analog-to-digital (ADC) 2014 that digitizes theanalog magnetic field signal. The output of the ADC 2014 is provided toa filter 2016 which is coupled to a controller 2018 that determines(e.g., using detectors or other circuitry) the positive peak (ppeak)value, the negative peak (npeak) value, the poscomp value and thenormalized value, all of which can be provided to the angle generationunit 2030. The magnetic field sensing element 2012 can be a Hall effectelement, GMR, or other appropriate sensing element.

The second channel 2020 includes a second magnetic field sensing element2022 coupled to an analog-to-digital (ADC) 2024 that digitizes theanalog magnetic field signal. The output of the ADC 2024 is provided toa filter 2026 which is coupled to a controller 2028 that determines(e.g., using detectors or other circuitry) the positive peak (ppeak)value, the negative peak (npeak) value, the poscomp value and thenormalized value, all of which can be provided to the angle generationunit 2030. The magnetic field sensing element 2022 can be a Hall effectelement, GMR, or other appropriate sensing element. It will beappreciated that the second channel 2020 can be a so-called “real”second channel or can be one or more virtual channel(s) generatedaccording to the techniques of the present disclosure, as described ingreater detail hereinbelow. The poscomp value can represent samples of asignal generated by comparing the digitized magnetic field signal to athreshold (referred to herein as a poscomp threshold).

The angle generation unit 2030 is configured to generate an angle signalfrom the first and second magnetic field signals generated by the firstand second magnetic field sensing elements 2012, 2022 or from a magneticfield signal as may be generated by the first magnetic field sensingelement and a virtual signal as may be generated based on the first andsecond magnetic field signals generated by the first and second magneticfield sensing elements, respectively. This can be accomplished, forexample, by calculating the arctangent of the magnetic field signals orby using a look-up table using values to determine the correspondingangle of the object.

The arctangent of the magnetic field signal divided by the otherquadrature (real or virtual) magnetic field signal can be used togenerate the angle signal. As will be appreciated in light of thepresent disclosure, the quotient of the two magnetic field signals (orone magnetic field signal and one virtual signal) at 90-degrees withrespect to each other provides what can be referred to as the “virtualtangent”, as illustrated according to Equations 1-11 below.

Since a virtual channel can be generated at any arbitrary phase over awide range of targets provided that the specific target (and thereforeits diameter and pole-pair count) is known, a virtual channel at −90°from the reference channel, L or CH1, can be generated as described inEquations 1 and 2, and as outlined hereinbelow regarding virtual channelsignal generation techniques:

$\begin{matrix}{L = {{A_{L} \cdot {\cos \left( {2\pi \; {ft}} \right)}} + O_{L}}} & {{Equation}\mspace{14mu} 1} \\{{VC}_{1} = {{A_{1} \cdot {\cos \left( {{2\; \pi \; {ft}} - \frac{\pi}{2}} \right)}} + O_{1}}} & {{Equation}\mspace{14mu} 2}\end{matrix}$

Note that the phase shift is negative as it will lag the referencechannel for forward motion. Notice that VC₁ can be simplifiedtrigonometrically as in Equation 3.

VC ₁ =A ₁·sin(2πƒt)+O ₁  Equation 3

Removing the offset (zeroing) and normalizing Equations 1 and 3 yieldsEquations 4 and 5.

$\begin{matrix}{X_{0} = {\frac{L - O_{L}}{A_{L}} = {\cos \left( {2\pi \; {ft}} \right)}}} & {{Equation}\mspace{14mu} 4} \\{X_{1} = {\frac{{VC}_{1} - O_{1}}{A_{1}} = {\sin \left( {2\pi \; {ft}} \right)}}} & {{Equation}\mspace{14mu} 5}\end{matrix}$

Equations 4 and 5 provide two possible quotients as illustrated inEquations 6 and 7.

$\begin{matrix}{\frac{X_{0}}{X_{1}} = {\frac{\cos \left( {2\pi \; {ft}} \right)}{\sin \left( {2\pi \; {ft}} \right)} = \frac{1}{\tan \left( {2{\pi ft}} \right)}}} & {{Equation}\mspace{14mu} 6} \\{\frac{X_{1}}{X_{0}} = {\frac{\sin \left( {2\pi \; {ft}} \right)}{\cos \left( {2\pi \; {ft}} \right)} = {\tan \left( {2{\pi ft}} \right)}}} & {{Equation}\mspace{14mu} 7}\end{matrix}$

Equations 6 and 7 are ultimately related as follows in Equations 8 and9.

$\begin{matrix}{{- {\tan \left( {\theta + \frac{\pi}{2}} \right)}} = {{- \left( \frac{\sin \left( {\theta + \frac{\pi}{2}} \right)}{\cos \left( {\theta + \frac{\pi}{2}} \right)} \right)} = {{- \left( \frac{\cos (\theta)}{- {\sin (\theta)}} \right)} = \frac{1}{\tan (\theta)}}}} & {{Equation}\mspace{14mu} 8} \\{{- {\tan \left( {\theta - \frac{\pi}{2}} \right)}} = {{- \left( \frac{\sin \left( {\theta - \frac{\pi}{2}} \right)}{\cos \left( {\theta - \frac{\pi}{2}} \right)} \right)} = {{- \left( \frac{- {\cos (\theta)}}{\sin (\theta)} \right)} = \frac{1}{\tan (\theta)}}}} & {{Equation}\mspace{14mu} 9}\end{matrix}$

As will be appreciated, a simple sign change and phase shift of ±90°will translate the two. In either case, then, the division of thenormalized and zeroed reference channel and virtual channel will yieldwhat can be called the “virtual tangent” of the target angle.

Having established the tangent of the target angle as described above,the target angle itself can be extracted by calculating (in real-time)the arctangent of it (see FIGS. 6-9, for example). Consider thearctangent of Equations 6 and 7 as resolved in Equations 10 and 11.

$\begin{matrix}{{\arctan \left( \frac{X_{1}}{X_{0}} \right)} = {{\arctan \left( {\tan \left( {2{\pi ft}} \right)} \right)} = {2{\pi ft}}}} & {{Equation}\mspace{14mu} 10} \\{{\arctan \left( \frac{X_{0}}{X_{1}} \right)} = {{\arctan \left( \frac{1}{\tan \left( {2{\pi ft}} \right)} \right)} = {{{- 2}{\pi ft}} \mp \frac{\pi}{2}}}} & {{Equation}\mspace{14mu} 11}\end{matrix}$

It is important to note that Equations 10 and 11 are more similar thanmight appear at first glance as the arctangent output exists on thewrapped interval

$\left\lbrack {{- \frac{\pi}{2}},\frac{\pi}{2}} \right\rbrack.$

The angle generation unit 2030 can further be configured to compare theangle signal to one or more angle signal thresholds to generate acorresponding plurality of output transitions, as described in greaterdetail herein. Each output transition can be indicative of the anglesignal crossing the corresponding angle signal threshold, and thus foreach period of the magnetic field signal, multiple output transitionscan be provided, improving the resolution and accuracy of the sensor.Refer, for example, to FIG. 3 showing an angle signal 3025 and fourcorresponding angle signal thresholds 3021, 3022, 3023, 3024.

The direction detection unit 2040 is configured to determine a directionof rotation of the object based on the angle signal generated by anglegeneration unit 2030. For example, the direction of rotation of theobject can be determined based on a polarity of a slope of the anglesignal. As another example, the direction of rotation can be determinedusing a plurality of comparators, where each magnetic field signal iscompared to a poscomp threshold to generate a respective square wavesignal, and the direction of rotation is determined by whether the firstsquare wave signal leads or lags the second square wave signal.

FIG. 2 shows a more detailed diagram of a dual-channel magnetic fieldsensor 2100 using an arbitrary number of switchpoints, according to thepresent disclosure. The sensor 2100 includes a first ADC 2114 thatreceives a magnetic field signal from a first (left, “L”) channel, whichis filtered by filter 2116 and provided to an amplifier 2117 so that itcan be used to generate a virtual channel. The output of the filter 2116is also provided to the reference channel controller 2118 which mayinclude a plurality of detectors for detecting the ppeak and npeakvalues, as well as processors or processing circuitry to determine theposcomp and norm values. The sensor 2100 also includes a second ADC 2124that receives a magnetic field signal from a second (right, “R”)channel, which is filtered by filter 2126 and provided to an amplifier2127 so that it can be combined with the output of the amplifier 2117 atcombiner 2128 and provided to virtual channel controller 2129. Thecontroller 2129 may include a plurality of detectors for detecting theppeak and npeak values, as well as processors or processing circuitry todetermine the poscomp and norm values. The output of amplifier 2117 andamplifier 2127 can be combined by combiner 2128 according to any of theappropriate techniques disclosed herein for generating virtual magneticfield signals. For example, refer to Equations 49 and 50 hereinbelowwhich may be used to determine coefficients that are used in generatingthe virtual channels. By calculating and solving for the coefficients inEquations 49 and 50, any number of arbitrary virtual signals can begenerated in accordance with the present disclosure. Thus, the virtualchannel, rather than or in addition to, the real reference channel canbe used to determine the speed and/or direction of rotation of theobject.

The normalized (“norm”) values from the reference channel controller2118 and the virtual channel controller 2129 can be provided to theangle generation unit 2130 to determine the angle of the objectproximate the sensor 2100. The angle can be determined, for example,using a CORDIC processor to compute the arctangent or a look-up table.The angle signal can be provided to the direction detection unit 2140 todetermine the direction of rotation and, in some cases, any vibration ofthe object. The direction “DIR” and high-resolution output “Hi res OUT”are provided to an output controller 2150, which may combine theinformation with poscomp ref from the reference channel 2118.

It will be appreciated that although a virtual channel that is at thedesired predetermined phase difference (e.g., quadrature at 90-degrees)with respect to the real, reference channel may be used as illustrated,if the magnetic field signals from the L and R channels are (or areclose to) 90-degrees phase separated with respect to each other, thevirtual channel could be eliminated and the real L and R channels couldbe used to perform the angle signal processing techniques according tothe present disclosure. It will likewise be appreciated that althoughonly one virtual channel is shown in FIG. 2, any number of virtualchannels can be implemented to further enhance the accuracy of thesystem, particularly when combined with the multiple angle signalthresholds applied to the angle signal, to provide a still furtherimproved accuracy of the system.

Although FIG. 2 illustrates one particular technique for generating avirtual signal that is quadrature, or substantially 90-degrees, withrespect to the real, reference signal, other techniques may beimplemented to generate two magnetic field signals that aresubstantially in quadrature with respect to each other. As such, twosignals could be used to generate the angle signal which can have asingle threshold or multiple thresholds applied thereto in order toprovide output transitions according to the present disclosure.

FIG. 3 shows example waveforms including input magnetic field signals ingraph 3000, normalized signals in graph 3010, an angle signal in graph3020, and associated output signal transitions in graph 3030 accordingto the present disclosure as may be generated by any of the sensors ofFIG. 1-2 or 10-10C. In particular, graph 3000 shows magnetic fieldsignals from the first or “left” channel 3002, the second or “right”channel 3004, and the virtual channel signal 3006, which is at90-degrees with respect to the first channel. These input signals 3002,3004 may be the signals generated by magnetic field sensing elements2012, 2022 in FIG. 1 for example. The virtual channel signal 3006 can begenerated from magnetic field signal 3002 and/or magnetic field signal3004, according to any of the various virtual channel signal generationtechniques disclosed herein.

Graph 3010 shows normalized signals with signal 3012 being a normalizedversion of the left channel signal 3002 and signal 3014 being anormalized version of the virtual channel signal 3006. The normalizedsignals shown in graph 3010 may correspond to the output of thecontroller for each channel, such as controller 2018, 2028 in FIG. 1, orthe output of controllers 2118, 2129 in FIG. 2. The normalized signalscan be made to have the same amplitude as each other or both can be madeequal to some other predetermined value.

Graph 3020 shows the angle signal 3025 that is generated from thenormalized signals 3012, 3014. The angle signal 3025 can be generated bycomputing the arctangent of the signals 3012, 3014 or with a look-uptable. The arctangent of the signals can be determined according to astandard CORDIC processing or according to arctangent calculatordisclosed herein (refer, for example, to FIGS. 6-9). In this example,there are four thresholds, including first threshold 3021, secondthreshold 3022, third threshold 3023, and fourth threshold 3024 whichare applied to the angle signal 3025. Note that by applying a pluralityof thresholds to the angle signal (which may be an arbitrary number ofthresholds), a greater number of output transitions can be provided foreach period (“T”) of the incoming magnetic field signal. For example,applying four thresholds results in four output pulses 3032, 3034, 3036,and 3038 during a single period T of the magnetic field signal as shown.Applying a greater number of thresholds to the angle signal 3025 allowsfor a greater number of output pulses to be generated during a singleperiod, thereby increasing the resolution and accuracy of the systemwithout significantly increasing the complexity of the system. Note thatFIG. 5 shows example graphs with 1, 2, 3, 4, or 5 thresholds applied,while FIG. 4 illustrates a method used to arrive at either the waveform3030 in FIG. 3 or waveform 5030 in FIG. 5.

Graph 3030 shows the output signal as a plurality of output transitions3032 through to 3040. Note that an output pulse is provided each timethat the angle signal 3025 crosses an angle signal threshold, with theoutput pulse 3032 corresponding to the angle signal 3025 crossing thefirst threshold 3021, the output pulse 3034 corresponding to the anglesignal 3025 crossing the second threshold 3022, the output pulse 3036corresponding to the angle signal 3025 crossing the third threshold3023, and the output pulse 3038 corresponding to the angle signal 3025crossing the fourth threshold 3024. As such, a greater number of pulsesis output by applying multiple thresholds to the angle signal. Due tothe angle signal 3025 being saw-toothed in shape, it lends itself toallowing multiple thresholds to be applied, or a single threshold at aprecise location, for example as discussed in connection with FIG. 5.

FIG. 4 is a flow diagram illustrating a method 4000 of generating aplurality of output transitions from applying a threshold to an anglesignal. At least one threshold, up to any arbitrary number ofthresholds, can be applied to the angle signal to achieve outputcommutations as desired, according to the present disclosure. The method4000 starts at 4010 by generating first and second magnetic fieldsignals having a predetermined phase difference with respect to eachother. These magnetic field signals may be real, measured magnetic fieldsignals or may be virtual magnetic field signals generated according toany of the various virtual magnetic field signal generation techniquesdisclosed herein (refer, for example, to FIGS. 10-23 showing varioussystems and methods for generating virtual magnetic field signals). Thefirst and second magnetic field signals are indicative of a magneticfield affected by an object. The first and second magnetic field signalsmay have a first predetermined phase difference with respect to eachother. The first and second magnetic field signals may be generated asvirtual magnetic field signals having a second predetermined phasedifference with respect to each other, which may be 90-degrees forexample. The virtual magnetic field signals may be generated accordingto a mathematical function that characterizes a relationship between thesecond predetermined phase difference between the virtual magnetic fieldsignals and the two measured magnetic field signals. Refer, for example,to equations 39-50 showing various mathematical functions that can beused to generate virtual magnetic field signals. The mathematicalfunction used to generate the virtual magnetic field signal(s) can bebased on a cosine of the second predetermined phase difference betweenthe virtual magnetic field signals and a sine of the secondpredetermined phase difference between the virtual magnetic fieldsignals (see. e.g., Equation 39 or Equations 49-50).

At block 4020, an angle signal is generated from the first and secondmagnetic field signals (which may be virtual magnetic field signals),the angle signal indicative of an angle of the magnetic field. Refer,for example, to graph 3020 in FIG. 3 showing angle signal 3025.

At block 4030, the angle signal is compared to at least one threshold togenerate a corresponding at least one output transition. Each outputtransition is indicative of the angle signal crossing a correspondingthreshold. Refer, for example, to graph 3030 in FIG. 3 showing anglesignal 3025 having a plurality of thresholds 3021, 3022, 3023, 3024 andan output signal is shown in graph 3040 having a plurality of outputtransitions 3032 through to 3040.

According to an angle signal threshold placement technique, in someapplications, it may be desirable to precisely locate the position ofthe angle signal threshold(s), which for example may depend upon adesired number of output transitions (or “output commutations” asinterchangeably referred to herein). The desired number of outputcommutations can be predetermined in some implementations, where adesired number of output commutations per pole-pair of the magneticfield signal is determined prior to processing the magnetic fieldsignals, or the desired number of output commutations can be determinedafter the magnetic field signals have been acquired and processed, aswill be appreciated.

FIG. 5 shows example waveforms including input magnetic field signals ingraph 5010, an angle signal in graph 5020, and associated output signaltransitions in graph 5030 according to the present disclosure as may begenerated by any of the sensors of FIG. 1-2 or 10-10C. In particular,graph 5010 shows magnetic field signals from the first or “left” channel5012, the second or “right” channel 5014, and the virtual channel signal5016, which is at 90-degrees with respect to the first channel. Theseinput signals 5012, 5014 may be the signals generated by magnetic fieldsensing elements 2012, 2022 in FIG. 1 for example. The virtual channelsignal 5016 can be generated from magnetic field signal 5012 and/ormagnetic field signal 5014, according to any of the various virtualchannel signal generation techniques disclosed herein.

Graph 5020 shows the angle signal 5022 generated from the magnetic fieldsignals 5012, 5014. The angle signal 5022 can be generated by computingthe arctangent of the signals 5012, 5014 or with a look-up table. Thearctangent of the signals can be determined according to a standardCORDIC processing or according to arctangent calculator disclosed herein(refer, for example, to FIGS. 6-9).

Graph 5030 shows the output signal as a plurality of output transitions,or commutations. Note that an output pulse is provided each time thatthe angle signal 5022 crosses an angle signal threshold with the numberof thresholds and placement of the threshold(s) depending upon a desirednumber of output commutations per pole-pair of the magnetic fieldsignal. Due to the angle signal 5022 being saw-toothed in shape, itlends itself to allowing multiple thresholds to be applied to the anglesignal 5022, as may be positioned at precise locations.

Note that the angle signal 5022 has wrapping points 5024, 5026, and 5028at the beginning and/or end of each period T of the angle signal. It maybe desirable to position the angle signal threshold(s) at some bufferdistance from the wrapping points in order to prevent outputcommutations near the wrapping points. Thus, a buffer region around thewrapping points of the angle signal can be maintained where no switchingoccurs (i.e., where no thresholds are placed). The position of the anglesignal threshold(s) can take into account various factors alone or incombination, including (1) the threshold(s) being equidistant and (2)the distance from any threshold(s) to a wrapping point of the anglesignal being maximized. Further, the number of output commutations perpole-pair, N_(OC) as referred to herein, should be an even integer dueto the natural arctangent wrapping of the angle signal. Each pole-pairof the angle signal, as will be appreciated, comprises two consecutivepoles (e.g., a pole-pair) of the rotating object, or two periods of theangle signal (with one period “T” as shown).

As described herein, with reference to Equations 10 and 11 copied below,the angle itself can be extracted by calculating the arctangent of thetangent, which is

${\frac{X_{0}}{X_{1}}\mspace{14mu} {or}\mspace{14mu} \frac{X_{1}}{X_{0}}},$

the first, real channel divided by the second, virtual channel, or viceversa, where X₀ and X₁ are the normalized and zeroed (zero meaned)versions of the real and virtual channels. As noted herein, thearctangent output exists in the wrapped interval

$\left\lbrack {{- \frac{\pi}{2}},\frac{\pi}{2}} \right\rbrack.$

Thus, it is desirable to ensure a buffer region at

$\left\lbrack {{- \frac{\pi}{2}},\frac{\pi}{2}} \right\rbrack,$

and multiples thereof. Given these constraints, the optimal thresholdvalues, T, are defined in Equations 12 and 13 below.

$\begin{matrix}{{k = {\frac{N_{OC}}{2} - 1}},\mspace{14mu} {N_{OC} = 2},4,6,\ldots} & {{Equation}\mspace{14mu} 12} \\{{{T\left( N_{OC} \right)} = {\left( \frac{\pi}{N_{OC}} \right) \cdot \left\{ {\tau_{0}\mspace{14mu} \ldots \mspace{14mu} \tau_{k}} \right\}}},{\tau_{i} = {{2 \cdot i} - k}}} & {{Equation}\mspace{14mu} 13}\end{matrix}$

where τ is the threshold number, k is the total number of thresholds,N_(OC) is the desired number of output transitions per pole-pair, and Tis the value of each threshold number that is to be applied to the anglesignal. For example, if the desired number of output transitions perpole-pair of the angle signal is 2, then k will be 2/2−1=0. Thus, therewill be only one threshold, with τ₀ being 2·0−0=0 and the thresholdvalue T will be

${\left( \frac{\pi}{2} \right) \cdot \left\{ 0 \right\}} = 0.$

Thus, for two output transitions per pole-pair, there will be onethreshold applied to the angle signal at zero, as shown in FIG. 5 andfurther articulated in the following equations.

Equations 12 and 13 can be used to derive several example terms fordetermining placement of the angle signal thresholds as demonstrated inEquations 14-18.

$\begin{matrix}{{T(2)} = {{\left( \frac{\pi}{2} \right) \cdot \left\{ 0 \right\}} = 0}} & {{Equation}\mspace{14mu} 14} \\{{T(4)} = {\left( \frac{\pi}{4} \right) \cdot \left\{ {{- 1},1} \right\}}} & {{Equation}\mspace{14mu} 15} \\{{T(6)} = {\left( \frac{\pi}{6} \right) \cdot \left\{ {{- 2},0,2} \right\}}} & {{Equation}\mspace{14mu} 16} \\{{T(8)} = {\left( \frac{\pi}{8} \right) \cdot \left\{ {{- 3},{- 1},1,3} \right\}}} & {{Equation}\mspace{14mu} 17} \\{{T(10)} = {\left( \frac{\pi}{10} \right) \cdot \left\{ {{- 4},{- 2},0,2,4} \right\}}} & {{Equation}\mspace{14mu} 18}\end{matrix}$

As shown in FIG. 5 and with reference to the Equations above, inEquation 14, when the desired number of output commutations (N_(OC)) isequal to two (2), using Equation 12, k will be 0 (2/2−1=0). Thus, therewill be one threshold for τ₀=0 (2×0−0). The threshold for τ₀ which usingequation 13 provides T (2)=2×0−0=0. Thus, when N_(OC) equals two (2),one threshold is applied at zero, which results in two outputcommutations (at 5031 and 5032).

Likewise, Equation 15 represents 4 output commutations (N_(OC)). Assuch, k will be 1 (4/2−1=1). Thus, there will be two thresholds, with τ₀being −1 and τ₁ being 1. As such, the thresholds for Equation 15 areprovided at

${{- \frac{\pi}{4}}\mspace{14mu} {and}\mspace{14mu} \frac{\pi}{4}},$

which results in four output commutations at 5041, 5042, 5043, and 5044.

Equation 16 represents six (6) output commutations (N_(OC)). As such, kwill be 2 (6/2−1=2). Thus, there will be three (3) thresholds, with τ₀being −2, τ₁ being 0, and τ₂ being 2. As such, the thresholds forEquation 16 are provided at

${- \frac{\pi}{3}},0,{{and}\mspace{14mu} \frac{\pi}{3}},$

resulting in six total output commutations at 5051, 5031, 5053, 5054,5032, and 5056.

Equation 17 represents eight (8) output commutations (N_(OC)). As such,k will be 3 (8/2−1=3). Thus, there will be four (4) thresholds, with τ₀being −3, τ₁ being −1, τ₂ being 1, τ₃ being 3. As such, the thresholdsfor Equation 17 are provided at

${- \frac{3\; \pi}{8}},{- \frac{\pi}{8}},0,\frac{\pi}{8},{{and}\mspace{14mu} \frac{3\; \pi}{8}},$

which results in eight output commutations at 5061, 5062, 5063, 5064,5065, 5066, 5067, and 5068.

Equation 18 represents ten (10) output commutations (N_(OC)). As such, kwill be 4 (10/2−1=4). Thus, there will be five thresholds, with τ₀ being−4, τ₁ being −2, τ₂ being 0, τ₃ being 2, τ₄ being 4, As such, thethresholds for Equation 18 are provided at

${- \frac{2\; \pi}{5}},{- \frac{\pi}{5}},0,\frac{\pi}{5},{{and}\mspace{14mu} \frac{2\pi}{5}},$

which results in ten output commutations at 5071, 5072, 5031, 5074,5075, 5076, 5077, 5032, 5079, and 5080.

Note that in each case the output equidistance is accurate to the orderof hundredths of a percent of the input frequency period.

Standard CORDIC processing can be used to generate the angle signal fromthe magnetic field signals, or a unique arctangent calculator, forexample as disclosed in FIGS. 6-9, according to the present disclosure.Note that although the arctangent calculation system disclosed herein isprimarily in relation to magnetic field signals, however it will beappreciated that the arctangent calculation system and method can beapplicable to any time-varying input signal to determine the arctangentthereof.

It is often desirable to calculate the arctangent of some real, timevarying function, ƒ(t):

y=arctan(ƒ(t))  Equation 19

While this function is well defined trigonometrically, calculating itaccurately over an arbitrary input range can be challenging. Its origincounterpart, tangent, ranges from negative to positive infinity forfinite inputs. Calculating the arctangent can be slow andcomputationally intensive when approached as a series approximation.However, an alternative approach is available, outlined in equations20-26. The following substitution enables working outside of the timedomain, briefly:

x=ƒ(t)  Equation 20

Substituting equation 20 into equation 19 and expanding it as anintegral-derivative pair in x yields Equation 21:

$\begin{matrix}{y = {{\arctan (x)} = {\int{\left( {\frac{d}{dx}\mspace{11mu} \arctan \; (x)} \right){dx}}}}} & {{Equation}\mspace{14mu} 21}\end{matrix}$

The derivative portion of Equation 21 is well defined in Equation 22:

$\begin{matrix}{{\frac{d}{dx}\; \arctan \; (x)} = \frac{1}{1 + x^{2}}} & {{Equation}\mspace{14mu} 22}\end{matrix}$

Substituting Equation 22 into Equation 21 yields Equation 23:

$\begin{matrix}{y = {{\arctan \; (x)} = {\int{\left( \frac{1}{1 + x^{2}} \right)\; {dx}}}}} & {{Equation}\mspace{14mu} 23}\end{matrix}$

In order to move Equation 23 back into the time domain, it is necessaryfirst to define dx in this domain. This can be readily accomplished bytaking the time derivative of Equation 23 and rearranging terms asillustrated in Equations 24 and 25.

$\begin{matrix}{\frac{dx}{dt} = {{\frac{d}{dt}{f(t)}} = {f^{\prime}(t)}}} & {{Equation}\mspace{14mu} 24} \\{{dx} = {{f^{\prime}(t)}{dt}}} & {{Equation}\mspace{14mu} 25}\end{matrix}$

Thus, an ultimately tractable form of the arctangent function is derivedin Equation 26, and the angle signal can be calculated according to amathematical function that integrates a time derivative of the anglesignal, for example as shown:

$\begin{matrix}{y = {{\arctan \left( {f(t)} \right)} = {\int{\frac{f^{\prime}(t)}{1 + {f^{2}(t)}}{dt}}}}} & {{Equation}\mspace{14mu} 26}\end{matrix}$

Reference is made to FIG. 6 showing a method of implementing anarctangent calculator according to the present disclosure, according toEquation 26. At block 610, the time derivative of the input signal isdivided by one plus the input signal squared to provide an output value

$\left( \frac{f^{\prime}(t)}{1 + {f^{2}(t)}} \right).$

At block 612, the output value is integrated as shown in Equation 26.

Thus, Equation 26 utilizes both time differentiation and integration.Differentiation in time and its real time discrete implementation aredescribed in Equations 27 and 28, respectively:

$\begin{matrix}{y = \frac{dx}{dt}} & {{Equation}\mspace{14mu} 27} \\{{Y\lbrack n\rbrack} = \frac{{X\lbrack n\rbrack} - {X\left\lbrack {n - 1} \right\rbrack}}{t_{s}}} & {{Equation}\mspace{14mu} 28}\end{matrix}$

Where t_(s) is the system sample time. Further, integration in time andits real time discrete implementation by forward Euler (see FIG. 7),backward Euler (see FIG. 8), or trapezoidal (see FIG. 9) methods aredescribed in Equations 29 through 32, respectively:

$\begin{matrix}{y = {\int{\times {dt}}}} & {{Equation}\mspace{14mu} 29} \\{{Y\lbrack n\rbrack} = {{Y\left\lbrack {n - 1} \right\rbrack} + {t_{s}{X\left\lbrack {n - 1} \right\rbrack}}}} & {{Equation}\mspace{14mu} 30} \\{{Y\lbrack n\rbrack} = {{Y\left\lbrack {n - 1} \right\rbrack} + {t_{s}{X\lbrack n\rbrack}}}} & {{Equation}\mspace{14mu} 31} \\{{Y\lbrack n\rbrack} = {{Y\left\lbrack {n - 1} \right\rbrack} + {\frac{t_{s}}{2}\left( {{X\lbrack n\rbrack} + {X\left\lbrack {n - 1} \right\rbrack}} \right)}}} & {{Equation}\mspace{14mu} 32}\end{matrix}$

FIG. 7 is a block diagram illustrating an arctangent calculation systemimplementing a forward Euler integrator, according to the presentdisclosure, corresponding to Equation 30.

FIG. 8 is a block diagram illustrating an arctangent calculation systemimplementing a backward Euler integrator, according to the presentdisclosure, corresponding to Equation 31.

FIG. 9 is a block diagram illustrating an arctangent calculation systemimplementing a trapezoidal integrator, according to the presentdisclosure, corresponding to Equation 32.

Selecting the most complicated case as an example, the trapezoidal caseas shown in FIG. 9, Equation 26 (duplicated below) can be implemented indiscrete time as follows in Equations 33 and 34:

$\begin{matrix}{\mspace{79mu} {y = {{\arctan \left( {f(t)} \right)} = {\int{\frac{f^{\prime}(t)}{1 + {f^{2}(t)}}{dt}}}}}} & {{Equation}\mspace{14mu} 26} \\{{Y\lbrack n\rbrack} = {{Y\left\lbrack {n - 1} \right\rbrack} + {\frac{t_{s}}{2}\left( {\frac{{F\lbrack n\rbrack} - {F\left\lbrack {n - 1} \right\rbrack}}{t_{s} \cdot \left( {1 + {F\lbrack n\rbrack}^{2}} \right)} + \frac{{F\left\lbrack {n - 1} \right\rbrack} - {F\left\lbrack {n - 2} \right\rbrack}}{t_{s} \cdot \left( {1 + {F\left\lbrack {n - 1} \right\rbrack}^{2}} \right)}} \right)}}} & {{Equation}\mspace{14mu} 33} \\{{Y\lbrack n\rbrack} = {{Y\left\lbrack {n - 1} \right\rbrack} + {\frac{1}{2}\left( {\frac{{F\lbrack n\rbrack} - {F\left\lbrack {n - 1} \right\rbrack}}{1 + {F\lbrack n\rbrack}^{2}} + \frac{{F\left\lbrack {n - 1} \right\rbrack} - {F\left\lbrack {n - 2} \right\rbrack}}{1 + {F\left\lbrack {n - 1} \right\rbrack}^{2}}} \right)}}} & {{Equation}\mspace{14mu} 34}\end{matrix}$

Notice that the requirement of including system sample time (t_(s))cancels itself out by simultaneously handling the discrete timedifferentiation and integration. Equation 35 below is a convenientsubstitution which simplifies the actual final implementation of thismethod for all integrator methods:

$\begin{matrix}{{A\lbrack n\rbrack} = \frac{{F\lbrack n\rbrack} - {F\left\lbrack {n - 1} \right\rbrack}}{1 + {F\lbrack n\rbrack}^{2}}} & {{Equation}\mspace{14mu} 35}\end{matrix}$

Thus, the final implementation for forward Euler, backward Euler, andtrapezoidal methods are described in Equations 36 through 38,respectively:

Y[n]=Y[n−1]+A[n−1]  Equation 36

Y[n]=Y[n−1]+A[n]  Equation 37

Y[n]=Y[n−1]+½(A[n]+A[n−1])  Equation 38

Where Equation 36 shows the forward Euler implementation as shown inFIG. 7, Equation 37 shows the backward Euler implementation as shown inFIG. 8, and Equation 38 shows the trapezoidal implementation as shown inFIG. 9.

The arctangent calculation system described herein can be implemented bycalculating real (measured) magnetic field signals, using one magneticfield signal and one or more virtual channel signals, or two or morevirtual channel signals. The virtual channel signals may be generatedaccording to any of the various virtual channel signal generationtechniques disclosed herein.

Although the dynamic output behavior of the arctangent calculator iscorrect, there may be some absolute error unless the integrator isinitialized to the correct value. This error could be minimized byinitializing to an approximation (some of which are relatively simple tocompute assuming the input meets certain conditions) or initializing tozero (the exact midrange value of arctangent function which exists onthe

$\left\lbrack {{- \frac{\pi}{2}},\frac{\pi}{2}} \right\rbrack$

interval).

Furthermore, during run time, any initial or accumulated error can bereset to zero by enforcing known state values as follows, as isnecessary to enforce the wrapping behavior of arctangent over the

$\left\lbrack {{- \frac{\pi}{2}},\frac{\pi}{2}} \right\rbrack$

interval:

${Y\lbrack n\rbrack} = {{- \frac{\pi}{2}}\mspace{14mu} {for}\mspace{14mu} {F\lbrack n\rbrack}\mspace{14mu} {at}\mspace{14mu} {negative}\mspace{14mu} {limit}}$Y[n] = 0  for  F[n] = 0  (or  zero  crossing)${Y\lbrack n\rbrack} = {\frac{\pi}{2}\mspace{14mu} {for}\mspace{14mu} {F\lbrack n\rbrack}\mspace{14mu} {at}\mspace{14mu} {positive}\mspace{14mu} {limit}}$

The following description in FIGS. 10-23 provides various systems andmethod for generating virtual magnetic field signals, which may includethe virtual magnetic field signals in FIGS. 10-12A and the correspondingdescription, virtual quadrature signals in FIGS. 13-21 and virtualarbitrary signals in FIGS. 22-23. These virtual signal generationtechniques can be used to generate virtual signals that are used ingenerating an angle signal, which can then be processed according to themultiple angle signal thresholding techniques of FIGS. 1-9.

Referring to FIG. 10, a magnetic field sensor 10 as may take the form ofa rotation detector can be used, for example, to detect passing gearteeth, for example, gear teeth 12 a-12 c of a ferromagnetic gear or,more generally target object 12. A permanent magnet 58 can be placed ata variety of positions proximate to the gear 12, resulting influctuations of a magnetic field proximate to the gear as the gearrotates. Use of the magnet 58 results in a so-called “back-bias”arrangement.

The sensor 10 can have a first terminal 14 coupled to a power supplydenoted as Vcc and a second terminal 16 coupled to a fixed voltage, forexample, a ground voltage, denoted as GND. A third terminal 18 of thesensor 10 permits communication of a sensor output signal 53 to circuitsand systems external to the sensor. The sensor output signal 53 can beprovided in the form of a voltage signal (as shown in FIG. 10) or acurrent signal. The illustrated sensor 10 can be considered athree-terminal device (i.e., a three-wire device) since it has thirdterminal 18 at which output signal 53 is provided. Sensor 10 can beprovided in the form of an integrated circuit (IC), with terminals 14,16, 18 provided by pins or leads of the IC.

The sensor 10 can include first, second, and third magnetic fieldsensing elements 20 a, 20 b, 20 c, respectively, here shown to be Halleffect elements. The first Hall effect element 20 a generates a firstdifferential voltage signal 24 a, 24 b, the second Hall effect element20 b generates a second differential voltage signal 26 a, 26 b, and thethird Hall effect element 20 c generates a third differential voltagesignal 28 a, 28 b, each having respective AC signal components inresponse to the rotating target 12.

While each one of the Hall effect elements 20 a, 20 b, 20 c is shown tobe a two terminal device, one of ordinary skill in the art willunderstand that each of the Hall effect elements 20 a, 20 b, 20 c isactually a four terminal device and the other two terminals of the Halleffect elements can be coupled to receive and pass respective currentsas might be provided, for example, by a current source or by a voltagesource (not shown).

First differential voltage signal 24 a, 24 b can be received by a firstdifferential preamplifier 30 a, the second differential voltage signal26 a, 26 b can be received by a second differential preamplifier 30 b,and the third differential voltage signal 28 a, 28 b can be received bya third differential preamplifier 30 c. First and second amplifiedsignals 32 a, 32 b generated by the first and second differentialpreamplifiers 30 a, 30 b, respectively, are received by a “right”channel amplifier 34 a and the second amplified signal 32 b and a thirdamplified signal 32 c generated by the second and third differentialpreamplifiers 30 b, 30 c, respectively, are received by a “left” channelamplifier 34 b. Designations of “right” and “left” are arbitrary.

A signal 38 a generated by the right channel amplifier 34 a is receivedby a right channel detector circuit 36 a and a signal 38 b generated bythe left channel amplifier 34 b is received by a left channel detectorcircuit 36 b. The signals 38 a, 38 b can be analog signals, generallysinusoidal in nature and further coupled to a controller 48 a. Signals38 a, 38 b are referred to herein generally as measured magnetic fieldsignals, which signals are indicative of a magnetic field affected bythe target object 12, such as by movement (e.g., rotation) of the target12. Thus, the sensor 10 can be considered to include a right processingchannel (or simply right channel) including amplifier 34 a and rightdetector circuit 36 a and a left processing channel (or simply leftchannel) including amplifier 34 b and detector circuit 36 b.

It will be appreciated that a “channel” refers generally to processingcircuitry associated with one or more magnetic field sensing elementsand configured to generate a respective channel signal. While theparticular processing circuitry shown in FIG. 10 to provide the rightchannel circuitry includes right channel amplifier 34 a and rightchannel detector circuit 36 a (and similarly the processing circuitryshown in FIG. 10 to provide the left channel circuitry includes leftchannel amplifier 34 b and left channel detector circuit 36 b), suchchannels can include less, more, or different processing circuitry.

Since the magnetic field sensing elements 20 a, 20 b that contribute tothe magnetic field signal 38 a are physically spaced from the magneticfield sensing elements 20 b, 20 c that contribute to the magnetic fieldsignal 38 b, it should be appreciated that the measured magnetic fieldsignals 38 a, 38 b are separated in phase. The phase difference, orseparation between magnetic field signals 38 a, 38 b can be based on thetarget feature size and the spacing between the magnetic field sensingelements 20 a-20 c. In embodiments, the phase separation between signals38 a, 38 b can be approximately ninety degrees (i.e., the signals can beapproximately in a quadrature relationship). However, it will beappreciated that other phase relationships between the magnetic fieldsignals are possible.

Furthermore, as will be explained below, while the physical separationof sensing elements 20 a-20 c and their differential coupling togenerate the measured magnetic field signals 38 a, 38 b illustrates oneway to generate phase separated measured magnetic field signals, otherconfigurations and techniques are also possible as shown for example inFIG. 10A and FIG. 10B. By way of non-limiting examples, channels can bebased on (i.e., can process) signals from independent (i.e., notdifferentially combined) magnetic field sensing elements and the phaseseparation of the resulting measured magnetic field signals can beachieved by the angular difference of the element positions and/or bythe use of different sensing element types having axes of maximumsensitivity in different planes (e.g., see FIG. 10A). In someembodiments, some channels can be based on signals from independentmagnetic field sensing elements and other channels can be based ondifferentially combined signals from a plurality of magnetic fieldsensing elements (e.g., FIG. 10B). Additional magnetic field sensingelement configurations can be found in a co-pending U.S. patentapplication Ser. No. 15/596,514 entitled “Magnetic Field Sensors andOutput Signal Formats for a Magnetic Field Sensor” filed on May 6, 2017assigned to the Assignee of the subject application and incorporated byreference herein in its entirety.

According to the disclosure, one or more virtual magnetic field signalsare generated in response to the measured magnetic field signals 38 a,38 b. Virtual magnetic field signal is used herein to describe a signalthat is indicative of a magnetic field affected by a target object, butwhich signal is computationally generated based on plurality of phaseseparated measured magnetic field signals which phase separated measuredmagnetic field signals are generated by one or more respective magneticfield sensing elements.

Taking the right channel detector circuit 36 a as representative of bothof the detector circuits 36 a, 36 b, the right channel detector circuit36 a includes a threshold detector circuit 40 a coupled to receive thesignal 38 a. The threshold detector circuit 40 a is configured to detectpositive and negative peaks of the signal 38 a, to identify apeak-to-peak value of the signal 38 a, and to generate a thresholdsignal 42 a that, for example, takes on a first threshold value at fortypercent of the peak-to-peak value of the signal 38 a and a secondthreshold value at sixty percent of the peak-to-peak value of the signal38 a. A comparator 44 a is coupled to receive the threshold signal 42 aand is also coupled to receive the signal 38 a. As a result, thecomparator 44 a generates a binary, two-state, signal 46 a that hastransitions when the signal 38 a crosses the first and second thresholds(e.g., “poscomp” thresholds as referred to herein).

A signal 46 b generated by the left channel detector circuit 36 b isgenerated in the same way as the signal 46 a. However, since themagnetic field sensing elements 20 a, 20 b contribute to the signal 46a, while the magnetic field sensing elements 20 b, 20 c contribute tothe signal 46 b, it should be appreciated that the signals 46 a, 46 bhave edges that differ in time (which is equivalent to phase for aparticular signal frequency, i.e., particular rotation speed). Thus, thedetector circuits 36 a, 36 b are configured to generate respective phaseseparated channel output, or speed signals 46 a, 46 b.

As will be explained, sensor 10 can generate additional channel outputsignals based on the one or more virtual magnetic field signals, as maybe referred to herein as virtual channel output signals (see FIGS. 11and 13 for example). These additional, virtual channel output signalscan be generated in a similar fashion to channel output signals 46 a, 46b, generally by comparison of virtual magnetic field signals to one ormore thresholds.

Movement speed of the target 12 can be detected in accordance with thefrequency of either of the phase separated channel signals 46 a, 46 b.In this way channel signals 46 a, 46 b can be considered to containredundant target speed information. It should be appreciated that adirection of rotation of the gear 12 may be determined from a relativephase or relative time difference (e.g., lag or lead) of a particularedge transition in the signal 46 a compared with a particularcorresponding edge transition in the signal 46 b. Therefore, a relativelag or a lead of edges of the signals 46 a, 46 b can be used to identifya direction of rotation of the gear 12.

While the sensor 10 is shown to include the detector circuits 36 a, 36b, each having a particular topology, described above as peak-to-peakpercentage detectors (threshold detectors), it should be understood thatany form of detectors may be used, such as peak-referenced detectors(peak detectors).

An output module 48 can include controller 48 a to receive and processthe phase separated measured magnetic field signals 38 a, 38 b andgenerate one or more virtual magnetic field signals based on themeasured magnetic field signals, as will be explained. Additionally,controller 48 a can generate one or more virtual channel output signalsbased on respective virtual magnetic field signals. The controller 48 ais further configured to generate sensor output signal 53 in a desiredformat, which output signal 53 may represent more than one signal. Forexample, output signal 53 may include one or more of channel outputsignals as two-state binary signals having a frequency indicative of thespeed of rotation of the target object, a direction signal indicative ofa direction of rotation of a target object and/or an exclusive OR (XOR)speed signal that provides a signal resulting from an XOR logicoperation based on the channel output signals. The channel outputsignals provided at the output of the sensor may include channel outputsignals 46 a, 46 b and additional channel output signals generated basedon respective virtual magnetic field signals as will be explained.

In the illustrated three wire sensor 10, the output driver 48 b may takethe form of an open-drain output. In this configuration, the driver 48 bmay include a bipolar transistor having a drain terminal coupled to Vccthrough a pull up resistor 62, as shown.

Referring also to FIG. 10A, an alternative magnetic field sensor 10′ asmay take the form of a rotation detector can be used to detect rotationof a ring magnet 60 having at least one north pole and at least onesouth pole. Thus, the sensor 10′ differs from the sensor 10 of FIG. 10in that the magnet 58 is omitted and gear 12 is replaced by ring magnet60.

The sensor 10′ further differs from the sensor 10 of FIG. 10 in thatsensor 10′ is a so-called two terminal device (or two-wire device), forwhich an output signal 52′ is provided in the form of a current at thetwo terminal power connection, superimposed upon the power supplyvoltage, Vcc, which current may be detected across a sense resistor 64.To this end, an output module 48′ can include a controller 48 a′ and anoutput driver 48 b′, as may take the form of voltage-controlled currentsource. Various circuitry is possible to implement the voltagecontrolled current source 48 b′ such as an operational amplifiercontrolling current through a pass element such as bipolar transistor.While the sense resistor 64 is shown coupled to the GND terminal 16, thesense resistor may alternatively be coupled to the Vcc terminal 14. Inembodiments in which the sensor 10′ is provided in the form of anintegrated circuit (IC), terminals 14, 16, are provided by pins or leadsof the IC.

The sensor 10′ further differs from the sensor 10 of FIG. 10 in thatsensor 10′ illustrates the use of independent, physically spaced apartmagnetic field sensing elements 20 a′, 20 b′. In embodiments, magneticfield sensing elements 20 a′, 20 b′ may take the form ofmagnetoresistance elements or other types of magnetic field sensingelements including Hall effect elements. For example, sensing elements20 a′, 20 b′ may each take the form of a bridge configuration containinga plurality of magnetoresistance elements, with each such bridgephysically spaced from the other. Alternatively, sensing elements 20 a′,20 b′ may each take the form of a different sensing element type, eachhaving an axis of maximum sensitivity in a plane that is orthogonal withrespect to the plane in which the axis of maximum sensitivity of theother element lies as illustrated in FIG. 10B. With this type ofarrangement, the phase separation of the resulting measured magneticfield signals can be achieved by the angular difference of the elementpositions and need not rely on the physical separation between theelements.

Each element 20 a′, 20 b′ can provide a respective differential signal24 a′, 24 b′, 28 a′, 28 b′ to a respective amplifier 30 a′, 30 b′ asshown. Amplifiers 30 a′, 30 b′ in turn can provide respective measuredmagnetic field signals 32 a′, 32 b′ to right and left detector circuits36 a, 36 b and to controller 48 a′, as shown. Measured magnetic fieldsignals 32 a′, 32 b′ may thus, be similar to phase separated measuredmagnetic field signals 38 a, 38 b of FIG. 10 and thus, may be used bycontroller 48 a′ to generate one or more virtual magnetic field signals.

Referring also to FIG. 10B, an alternative magnetic field sensor 100includes a digital controller 110. Sensor 100 can take the form of arotation detector to detect rotation of a target (e.g., gear 12 of FIG.10 or ring magnet 60 of FIG. 10A) and provide one or more output signals112 a, 112 b containing speed, direction, vibration, or other targetinformation.

Sensor 100 illustrates a magnetic field sensing element configurationincluding one or more first sensing elements 118 a, 118 b each having anaxis of maximum sensitivity in a first plane and one or more secondsensing elements 120 having an axis of maximum sensitivity in a secondplane generally orthogonal with respect to the first plane. As oneexample, as illustrated, the first sensing elements 118 a, 118 b may beplanar Hall effect elements and the second sensing element 120 may takethe form of one or more magnetoresistance elements. Outputs of sensingelements 118 a, 118 b can be differentially combined by amplifier 122 aand outputs of sensing element 120 can be provided to amplifier 122 b togenerate respective measured magnetic field signals 124 a, 124 b. Withthis type of arrangement, the phase separation of the resulting measuredmagnetic field signals 124 a, 124 b can be achieved by use of thedifferent types of sensing elements having axes of maximum sensitivityin different planes and need not rely on the physical separation betweenthe elements.

Processing of the measured magnetic field signals 124 a, 124 b caninclude offset adjustment by modules 126 a, 126 b, automatic gaincontrol by elements 130 a, 130 b, filtering by filters 134 a, 134 b, andanalog-to-digital conversion by ADCs 138 a, 138 b. The resultingmeasured magnetic field signals 140 a, 140 b thus processed are coupledto digital controller 110 as shown.

Digital controller 110 is configured to generate one or more virtualmagnetic field signals based on the measured magnetic field signals 140a, 140 b. To this end, controller 110 can include a virtual signalgenerator 142, the operation of which will be described further below.Controller 110 can be further configured to generate one or more channeloutput signals 150 a, 150 b that may be the same as or similar tochannel output signals 46 a, 46 b of FIG. 10. To this end, controller110 can include a detector 144 that may provide functionality similar toor the same as detectors 36 a, 36 b of FIG. 10 and a threshold generator146 that may provide functionality similar to or the same as thresholddetectors 40 a, 40 b of FIG. 10. Memory 148, such as EEPROM, can be usedto store values for use by the virtual signal generator 142 and thedetector 144 for example.

One or more output signals of controller 110 can include channel outputsignals 150 a, 150 b that may be the same as or similar to channeloutput signals 46 a, 46 b (FIG. 10), a direction signal 152 indicativeof a direction of rotation of a target, and an XOR speed signal 154indicative of an exclusive-OR combination of channel output signals 150a, 150 b for example. Additional output signals can be provided on theillustrated or additional signal lines and can include additionalchannel output signals based on the one more virtual measured magneticfield signals. These new additional output switching locations can alsobe incorporated into the existing output signals through the use oflogic gates to provide higher resolution position information withoutthe need for additional output pins on the IC. In general, the number ofoutput signal switching events can be referred to as “outputcommutations” and with generation of virtual magnetic field signals, anydesired number of output commutations per pole-pair of the target objectcan be achieved.

Referring also to FIG. 10C, another alternative magnetic field sensor170 includes a digital controller 180. Sensor 170 includes a magneticfield sensing element configuration like FIG. 5 and thus includes Halleffect elements 170 a, 170 b, 170 c, each providing an output signal toa respective differential amplifier 172 a, 172 b to generate respectivemeasured magnetic field signals 174 a, 174 b, as shown. The phasedifference, or separation between measured magnetic field signals 174 a,174 b can be approximately ninety degrees (i.e., the signals can beapproximately in a quadrature relationship).

Processing of the measured magnetic field signals 174 a, 174 b can beperformed more in the digital domain than in the embodiment of FIG. 10B.Accordingly, measured magnetic field signals 174 a, 174 b can beconverted to respective digital signals by ADCs 176 a, 176 b, as shown.Offset adjustment, gain control, filtering and other types of signalprocessing functionality can be implemented by controller 180.

Digital controller 180 is configured to generate one or more virtualmagnetic field signals based on the measured magnetic field signals 178a, 178 b. To this end, controller 180 can include a virtual signalgenerator 182, the operation of which will be described further below.Controller 180 can be further configured to generate one or more channeloutput signals that may be the same as or similar to channel outputsignals 46 a, 46 b of FIG. 10. To this end, controller 180 can include adetector 184 that may provide functionality similar to or the same asdetectors 36 a, 36 b of FIG. 1 and a threshold generator 186 that mayprovide functionality similar to or the same as threshold detectors 40a, 40 b. Memory 188, such as EEPROM, can be used to store values for useby the virtual signal generator 182 and the detector 184 for example.

One or more output signals 190 a, 190 b of controller 180 can includechannel output signals that may be the same as or similar to channeloutput signals 46 a, 46 b (FIG. 10), a direction signal indicative of adirection of rotation of a target, and an XOR speed signal indicative ofan exclusive-OR combination of channel output signals for example.Additional output signals can be provided on the illustrated oradditional signal lines and can include additional channel outputsignals based on the one more virtual measured magnetic field signals.These new additional output switching locations can also be incorporatedinto the existing output signals through the use of logic gates toprovide higher resolution position information without the need foradditional output pins on the IC. Controller output signals 190 a, 190 bcan be coupled to respective output drivers 192 a, 192 b to providesensor output signals 194 a, 194 b containing desired information in adesired format.

Referring to FIG. 11, generation of a virtual magnetic field signal 204as may be achieved by any of the above-described sensors 10, 10′, 100,170 (see FIGS. 10-10C, respectively) is illustrated. Virtual magneticfield signal 204 is shown along with measured magnetic field signals 208a, 208 b in waveforms 200 against a horizontal axis representing anglein units of degrees and a vertical axis in normalized units of volts.

A target 210 as may be similar to the gear 12 of FIG. 10 includesfeatures 210 a, 210 b such as may represent gear teeth for example. Themechanical profile of target 210 that reflects the target geometry isrepresented by waveform 214 having a horizontal axis representing anglein the same units of degrees as waveforms 200.

As the target 210 rotates and features 210 a, 210 b pass the pluralityof sensing elements of the sensor, measured magnetic field signals 208a, 208 b are generated. For example, measured magnetic field signals 208a, 208 b can correspond to signals 38 a, 38 b of FIG. 10. Thus, it canbe seen that the phase separation of measured magnetic field signals 208a, 208 b (referred to herein as a first predetermined phase difference)can be on the order of ninety degrees.

Operate and release threshold levels 220 a, 220 b (i.e., BOP, BRP,respectively) are shown in relation to the measured magnetic fieldsignals 208 a, 208 b. As an example, the BOP threshold level 220 a canrepresent a first percentage (e.g., 60%) of the peak-to-peak value ofmagnetic field signal 208 a and the BRP threshold level 220 b canrepresent a second, different percentage (e.g., 40%) of the peak-to-peakvalue of magnetic field signal 208 a. Other threshold levels arepossible including but not limited to other percentages of thepeak-to-peak magnetic field signal, thresholds that are a predeterminedpercentage or a predetermined absolute difference with respect topositive and negative peaks of the magnetic field signal, etc.

By operation of detector circuitry (e.g., by detector circuits 36 a, 36b of FIG. 10 or controller 110 of FIG. 10B for example), channel outputsignals 230 a, 230 b based on respective measured magnetic field signals208 a, 208 b are generated. When measured magnetic field signal 208 acrosses the BRP threshold level 220 b, the respective channel outputsignal 230 a transitions, here to a logic high level, and when measuredmagnetic field signal 208 a crosses the BOP threshold level 220 a, therespective channel output signal 230 a transitions, here to a logic lowlevel. Channel output signal 230 b is generated in a similar mannerbased on crossings of the measured magnetic field signal 208 b with theBOP threshold level 220 a and the BRP threshold level 220 b, as shown.The result is channel output signals 230 a, 230 b based on respectivemeasured magnetic field signals 208 a, 208 b, which channel outputsignals which have a phase separation relative to one another that isestablished by the phase separation between the measured magnetic fieldsignals 208 a, 208 b. Thus, the channel output signals 230 a, 230 b havethe same predetermined phase separation with respect to each other asthe measured magnetic field signals 208 a, 208 b have with respect toeach other.

By operation of a controller (e.g., 48 a, 48 a′, 110, 180), virtualmagnetic field signal 204 is generated based on the measured magneticfield signals 208 a, 208 b with a second predetermined phase differencewith respect to at least one of the signals 208 a, 208 b. Inembodiments, the second predetermined phase difference can be withrespect to each of the measured magnetic field signals 208 a, 208 bresulting in the virtual signal 204 being evenly spaced with respect toboth signals 208 a, 208 b. In other embodiments, the virtual signal 204can be unevenly spaced with respect to signals 208 a, 208 b (i.e.,virtual signal 204 can be closer to signal 208 a than it is to signal208 b).

The sensor may be user programmable to select a desired number ofvirtual magnetic field signals to be generated and also to select thedesired phase difference between the virtual magnetic field signal(s)and the measured magnetic field signals. For example, the sensor maypermit a user to select a desired resolution and, on that basis, thecontroller can determine how many virtual magnetic field signals will begenerated and their respective phases, as will be illustrated inconnection with FIG. 13.

Detector circuitry and techniques can be used to process the virtualmagnetic field signal 204 to generate a respective virtual channeloutput signal 234 based on crossings of the virtual magnetic fieldsignal 204 with the threshold levels 220 a, 220 b. When virtual magneticfield signal 204 crosses the BRP threshold level 220 b, the respectivevirtual channel output signal 234 transitions, here to a logic highlevel, and when virtual magnetic field signal 204 crosses the BOPthreshold level 220 a, the respective virtual channel output signal 234transitions, here to a logic low level, as shown.

Referring also to the flow diagram of FIG. 12, a method 300 ofgenerating a virtual magnetic field signal begins at block 302,following which at least two measured magnetic field signals having afirst predetermined phase difference with respect to each other aregenerated in block 304. Generating the magnetic field signals may beaccomplished with magnetic field sensing elements, such as the Halleffect elements 20 a, 20 b, 20 c of FIGS. 10 and 10A or themagnetoresistance elements 20 a′, 20 b′ in FIG. 10B, for example.

In block 306 (as shown in more detail in FIG. 12A), the phase separatedmeasured magnetic field signals are used to generate at least onevirtual magnetic field signal having a second predetermined phasedifference with respect to at least one of the magnetic field signals,as may be accomplished with sensor controller circuitry and techniques.The measured and virtual magnetic field signals can be processed bydetector circuitry and techniques to generate respective channel outputsignals for communicating high resolution information (referred togenerally as output commutations) about the target angle for example.

An example subprocess for generating the virtual magnetic field signalis illustrated by the flow diagram of FIG. 12A and can include the useof a mathematical function that characterizes a relationship between thesecond predetermined phase difference and the measured magnetic fieldsignals. For example, values of the virtual magnetic field signal can becomputed according to the following mathematical function, Equation 39:

cos(phase)*Ch1+sin(phase)*Ch2  Equation 39

where “phase” represents the second predetermined phase separationbetween the virtual magnetic field signal and the measured magneticfield signals relative to a single period of the measured magnetic fieldsignal (e.g., a target rotation from an edge of one feature to a likeedge of the next feature). Thus, in the example of FIG. 11, where it isdesired to generate a single virtual magnetic field signal 204 evenlyspaced between signals 208 a, 208 b, “phase” is given by 45°. In theabove function, “Ch1” represents the magnitude of one of the measuredmagnetic field signals (e.g., 208 a) and “Ch2” represents the magnitudeof the other one of the measured magnetic field signals (e.g., 208 b).

The subprocess 350 of FIG. 12A begins at block 352. In block 356, thecosine of the second predetermined phase is determined and in block 358,the sine of the second predetermined phase is determined. Variouscomponents and techniques can be used to determine the desired sine andcosine values. In an example embodiment, a look-up table (as may bestored in EEPROM for example) is used to determine the cosine and sinevalues. This type of configuration can be desirable in sensorscontaining binary digital logic since sine and cosine functioncomputations can be difficult to implement. In other embodiments, suchas those containing a microprocessor, the sine and cosine values can becomputed directly.

Considering embodiments using a look-up table (Table 1) to determine thedesired sine and cosine values, contents of an example look-up table canbe given by the following:

TABLE 1 Binary Binary equivalent equivalent of of Approximateapproximate Approximate approximate decimal decimal decimal decimalvalue of value of cos value of value of sin Virtual Cos (virtual cos(virtual (virtual Sin (virtual sin (virtual (virtual Phase phase) phase)phase) phase) phase) phase) 30 0.866 0.8125 0.1101 0.5 0.5 0.1000 450.707 0.6875 0.1011 0.707 0.6875 0.1011 60 0.5 0.5 0.1000 0.866 0.81250.1101 120 −0.5 −0.5 −0.1000 0.866 0.8125 0.1101 135 −0.707 −0.6875−0.1011 0.707 0.6875 0.1011 150 −0.866 −0.8125 −0.1101 0.5 0.5 0.1000

In an implementation containing a look-up table, a binary equivalent ofa decimal approximation of the desired sine and cosine values can beused. For example, considering generation of the virtual magnetic fieldsignal 204 (FIG. 11) in which the desired virtual phase is 45°, in block356 binary equivalent value 0.1011 of the cosine of 45° can bedetermined. In block 358, binary equivalent value of 0.1011 of the sineof 45° can be determined.

Furthermore, because the cosine values can be negative for some desiredphase separations of the virtual magnetic field signal, the ADC(s) thatconvert the measured magnetic field signals to digital values can beoffset such that a midpoint of available codes corresponds to zero. Forexample, in the case of a 12-bit ADC providing 4096 codes, the midpointcode of 2048 can be used to represent zero volts.

Having thus determined the cosine and sine values for the desired phasefor the virtual signal being generated, the binary equivalent value canprovide a fixed coefficient for use in subsequent process blocks 360,362. In block 360, the cosine value thus determined is multiplied by thevalue of one of the measured magnetic field signals (e.g., Ch1 as maycorrespond to signal 208 a) and in block 362, the sine value thusdetermined is multiplied by the value of the other one of the measuredmagnetic field signals (e.g., Ch2 as may correspond to signal 208 b). Inblock 364, the products determined in blocks 360 and 362 are added tothereby determine the corresponding value of the virtual magnetic fieldsignal (e.g., signal 204) and the subprocess ends at block 366.

Referring also to FIG. 13, example waveforms 400 are shown in connectionwith a sensor generating more than one virtual magnetic field signal,and here four virtual magnetic field signals 410 a, 410 b, 410 c, 410 d.Also shown are measured magnetic field signals 402 a, 402 b against ahorizontal axis representing angle in units of degrees and a verticalaxis in normalized units of volts.

In the example of FIG. 13, each of the virtual magnetic field signals410 a-410 d is evenly spaced between the measured magnetic field signals402 a, 402 b. Thus, the phase separation between each consecutive signal402 a, 402 b, 410 a, 410 b, 410 c, and 410 d is 30°.

The number of virtual signals and the phase separation between thevirtual signals can be determined by the sensor controller in responseto a user selection of a programming option. In the illustrated example,the user may have selected to receive twelve edges for each period, orgear tooth for example. With such resolution selected and based onknowledge of the target (i.e., how many periods the target represents),the sensor controller can determine that four virtual magnetic fieldsignals with a phase separation of 30° between each other and betweeneach of the measured magnetic field signals should be generated.Alternatively, a user can provide a “resolution improvement factor”where the standard 4 edges per period generated by the physical channelscould be scaled by 2× (resulting in 8 edges) or 3× (resulting in 12edges) by using added virtual channels.

By detector operation, each of the magnetic field signals 402 a, 402 b,410 a, 410 b, 410 c, and 410 d can be processed to generate a respectivechannel output signal according to threshold crossings as discussedabove. For example, measured magnetic field signals 402 a, 402 b can beused to generate respective channel output signals 416 a, 416 b andvirtual magnetic field signals can be used to generate respectivevirtual channel output signals 422 a, 422 b, 422 c, and 422 d.

Consideration of the measured channel output signals 416 a, 416 breveals that, for each period (i.e., from one target tooth edge to thelike edge of the next tooth), four switch events (i.e., four transitionsof measured channel output signals 416 a, 416 b) occur. By contrast, useof both the measured channel output signals 416 a, 416 b and the fourvirtual channel output signals 422 a, 422 b, 422 c, 422 d results intwelve switch events per period. Accordingly, a 3x improvement in targetsensing resolution is achieved.

It will be appreciated that in applications in which the required numberof virtual signals is an odd number, the measured channel output signalsmay not be used for target detection. In other words, if the number ofvirtual signals is such that their even phase separation within each360° period would result in uneven phase separation with respect to themeasured magnetic field signals, then only the virtual channel outputsignals may be used to control the target. For example, if the userprogrammed resolution and target are such as to require that fivevirtual magnetic field signals be generated at relative phases of 72°,144°, 216°, 288°, and 360°, then the measured magnetic field signals atapproximately 0° and 90° can be ignored for target control purposes.

Also illustrated in FIG. 13 are two direction changes which canrepresent a change in the direction of rotation of the target. As notedabove, the relative lead or lag of edges of the channel output signalscan be used to determine the direction of rotation of the target. Theincreased target detection resolution provided by the virtual channeloutput signals 422 a, 422 b, 422 c, 422 d can result in a more rapiddetermination of a direction change than otherwise possible.

It will be appreciated that the aforementioned virtual signal generationassumes that the measured magnetic field signals used to generate thevirtual magnetic field signals have a perfect quadrature relationship(i.e., there is no “phase error” or deviation from perfect quadraturebetween the first and second measured magnetic field signals).Traditionally, the only way to ensure sensor outputs in quadrature wasto mechanically position two sensors on difference phases (positions) ofthe target, or to use a single IC solution with two channels in a singleIC and have the target designed to have a period exactly two times themechanical separation of the channels in the IC. This requires a veryspecific sensor configuration that is not readily applicable to multipletarget environments. As a result, the phase difference of the measuredmagnetic field signals may not be 90-degrees (i.e., there may be a phaseerror between the measured magnetic field signals) in which case errorscan occur when determining wheel displacement or other calculationsbased on the virtual magnetic field signals.

FIG. 14 shows example waveforms of two measured magnetic field signals510, 512 and two virtual magnetic field signals 514, 516 generated fromthe measured magnetic field signals 510, 512 in the manner set forthabove where the measured magnetic field signals 510, 512 are inquadrature. Also shown in FIG. 14 are channel output signals in the formof output pulses 520 a-520 h based on each of the measured and virtualmagnetic field signals 510, 512, 514, 516 crossing a threshold (e.g.,“poscomp” threshold as described herein). As is apparent, the outputpulses 520 a-520 h are equally spaced apart. This equidistant outputpulse spacing is achieved by virtual signals 514, 516 being precisely90-degrees with respect to each other and precisely 30-degrees withrespect to each measured magnetic field signal 510, 512. It will beappreciated that although the illustrated output pulses 520 a-520 hcorrespond to the zero crossing points of measured magnetic fieldsignals 510, 512 and the virtual magnetic field signals 514, 516, otherthreshold levels could be used.

As shown for example in FIG. 15, providing a channel output signal 610with equidistant output pulses 520 a-520 h allows for processing of themagnetic field signals without error, or with minimal error, as shownfor example in FIG. 15. Also shown in FIG. 15 is wheel displacement 612,and wheel displacement error 614, where there is no phase error betweenthe first and second measured magnetic field signals. As shown in graph610, by providing equidistant output pulses 520 a-520 g, the wheeldisplacement 620 in graph 612 is equally stepped through the positions,and the resulting graph 614 shows no wheel displacement error.

FIG. 16 shows example waveforms of two measured magnetic field signals710, 712 having a 30-degree phase error between the measured magneticfield signals 710, 712, and two virtual magnetic field signals 714, 716generated from the measured magnetic field signals 710, 712 in themanner described above. As is apparent, the resulting channel outputsignal pulses 720 a-720 g are not equidistant, which can result in wheeldisplacement error, as shown in FIG. 17. Furthermore, when the measuredmagnetic field signals 710, 712 are not in perfect quadrature, theamplitude of the resulting virtual signals 714, 716 will not match theamplitude of the measured magnetic field signals 710, 712, as shown.

FIG. 17 shows example waveforms of the output signal 810 includingnon-equidistant pulses 720 a-720 h, wheel displacement 812, and wheeldisplacement error 814, where there is a 30-degree phase error betweenthe measured magnetic field signals 710, 712. Also shown in graph 810are ideal output pulses 820 a-820 e (pulses 820 a, 820 b, 820 c, 820 d,and 820 e at the ideal locations). The actual wheel displacement 830 andideal wheel displacement 832 are shown in graph 812. This discrepancyresults in a wheel displacement error shown in graph 814. The wheeldisplacement error signal 840 has several locations 840 a, 840 b, 840 c,840 d, 840 e, and 840 f, where there is an error due to the outputpulses 720 a-720 h not being equidistant in spacing.

Thus, in order to minimize processing errors, it is important for themeasured and/or virtual magnetic field signals to have a predeterminedphase separation with respect to each other. In some instances, themeasured magnetic field signals will have a quadrature relationship andthus, the virtual magnetic field signals based on such quadraturesignals will have the desired, predetermined phase separation withrespect to the measured magnetic field signals and to each other.

Rather than relying on the measured magnetic field signals to have thedesired quadrature relationship, according to a further aspect, virtualquadrature magnetic field signals (or simply referred to herein as“virtual quadrature signals”) can be computationally generated to have aquadrature relationship with respect to at least one of the measuredmagnetic field signals, which measured magnetic field signals need notbe in perfect quadrature. FIGS. 18-21 are associated with generatingvirtual quadrature magnetic field signals.

As another alternative to relying on the measured magnetic fieldssignals to have the desired quadrature relationship, according to afurther aspect, generating virtual magnetic field signals can be basedon the use of generalized coefficients. The resulting virtual magneticfield signals can be referred to as virtual arbitrary magnetic fieldsignals or simply referred to herein as “virtual arbitrary signals”since these generated virtual signals need not have a quadraturerelationship as will result from the process of FIG. 21 for example.Generation of such virtual arbitrary signals is described below inconnection with FIGS. 22-23.

It may be desirable to generate virtual signals that are at apredetermined 90-degree phase difference with respect to each other,referred to herein as virtual quadrature signals. These virtualquadrature signals can be used in further processing of FIGS. 10-13.FIG. 18 is a diagram of an example virtual signal generator 182′ forgenerating virtual quadrature signals, according to the disclosure. Thevirtual signal generator 182′ can be the same as, or similar to, thevirtual signal generator 182 shown in FIG. 10C, or the virtual signalgenerator 142 shown in FIG. 10B and can be configured to generate bothvirtual magnetic field signals (e.g., FIGS. 10-13) and the virtualquadrature signals (e.g., FIGS. 18-21). The virtual signal generator182′ is configured to use an averaging unit 910, a differencing unit912, and an optional amplitude correction unit 914 to generate thevirtual quadrature signals (refer, for example, to FIG. 19 showingexample virtual quadrature signals 1020, 1022).

Virtual quadrature signals 1020, 1022 can be generated by calculatingthe average of two input signals (e.g., measured magnetic field signals1010, 1012 of FIG. 19) to generate a 0-degree reference basis signal(the first virtual quadrature signal) and then calculating thedifference of the two input signals to generate a 90-degree out-of-phasesignal (the second virtual quadrature signal). The 90-degreeout-of-phase signal can be amplitude-adjusted to match the 0-degreereference to provide consistent amplitudes between signals as will beexplained. These virtual quadrature signals can further provide thestarting point for generating other virtual signals in accordance with,for example, FIGS. 10-13.

When signals are generated by a sensor that has been implemented as anintegrated circuit (IC), the position of the sensing elements iscritical in performing processing of signals generated by the sensingelements. By mathematically generating virtual quadrature signals, themechanical separation (and physical location) of the sensing elements inthe IC does not have to be matched or otherwise tuned to the targetbeing sensed, allowing for a single IC to be used with many differenttarget geometries. The virtual quadrature signals provide optimal sensoroutputs to be used for direction detection, accurate phase calculation,and further virtual signal generation.

The averaging unit 910 computes the average, Z, of the two measuredmagnetic field signals according to Equation 40:

$\begin{matrix}{Z = \frac{A + B}{2}} & {{Equation}\mspace{14mu} 40}\end{matrix}$

where A is the measured magnetic field signal of the first channel and Bis the measured magnetic field signal of the second channel. By addingthe two measured magnetic field signals A and B together, and thendividing by two, the first virtual quadrature signal (at zero-degrees)is generated. For digital signals, dividing the signals by twoessentially entails truncating the last bit of each digital signal andthen adding the two signals. For analog signals, the values are addedand divided by two to determine the average. This average provides thevirtual 0-degree quadrature signal (the first virtual quadraturesignal).

The differencing unit 912 computes the difference, Vi of the twomeasured magnetic field signals according to Equation 41:

V={[(B−X)−(A−X)]×K}+X  Equation 41

where A is the measured magnetic field signal of the first channel, B isthe measured magnetic field signal of the second channel, X is themidpoint between the total number of possible codes, and K is anamplitude correction factor. The total number of possible “codes” refersto the maximum number of least significant bits (LSB) of an ADC of thesensor (e.g., ADC 176 a, 176 b in FIG. 10C, or 138 a, 138 b in FIG.10B). When the values of the first channel A and the second channel Bare digital values, calculating the difference requires elimination ofthe fixed offset that centers the signal inside the middle of the ADCrange, and this center or “midpoint” needs to be considered. Thus, themidpoint ‘X’ is subtracted from each channel (B-X) for the secondchannel, and (A-X) for the first channel, and then the midpoint X isadded back in after the value for each channel is multiplied by theamplitude correction factor K. Alternatively, if the values for eachchannel A and B are analog values, the values can simply be subtractedfrom each other and then multiplied by an amplitude correction factor K.Calculating the difference according to Equation 41 provides the virtual90-degree out-of-phase quadrature signal (the second virtual quadraturesignal).

FIG. 19 shows example waveforms of measured magnetic field signals 1010and 1012 and two virtual quadrature magnetic field signals 1020 and 1022that are generated according to the disclosure. The averaging unit 910from FIG. 18 generates the first virtual 0-degree quadrature signal 1020and the differencing unit 912 (with optional amplitude correction unit914) generates the second virtual 90-degree quadrature signal 1022.Advantageously, the measured magnetic field signals 1010, 1012 can haveany phase difference with respect to each other.

FIG. 20 shows an example waveform for an amplitude correction curve 1110that can be used in generating virtual quadrature signals. In someinstances when the measured magnetic field signals used to generate thevirtual quadrature signals are not in perfect quadrature, themathematical calculations used to generate the virtual quadraturesignals may not result in signals that have the same amplitude. This canbe accounted for through further processing that determines the signalamplitudes before generating switching thresholds, or it can becompensated for by applying an amplitude correction to the differencechannel (the virtual 90-degree channel) for example using a curve, suchas curve 1110.

The amplitude correction curve represents the ratio between the averagesignal and the difference signal and is used to ensure that theamplitude of both virtual quadrature signals is the same as (orsubstantially equal to) the amplitude of the measured magnetic fieldsignals. In embodiments, the amplitude correction curve 1110 has asubstantially exponential shape, as shown. Because of the exponentialnature of the amplitude correction curve 1110, a mathematical correctioncan be complicated to perform with basic digital logic circuits. Inembodiments, the correction curve 1110 can be approximated by linearsegments A, B, C, D, and E that correspond to segments of the curve1110. Thus, simpler binary multiplication can be performed toapproximate the exponential curve, for example as shown in the Table 2below:

TABLE 2 Segment A B C D E Decimal 1.5 1.25 1 0.75 0.625 Factor Binary1.100 1.010 1.000 0.110 0.101 Equivalent

Table 2 can be used as a look-up table for determining the appropriatebinary equivalent for a decimal factor of the curve. The amplitudecorrection factor is variable K in Equation 41 above and used incalculating the 90-degree (“second”) out-of-phase virtual quadraturesignal.

If the amplitudes of the virtual signals start to deviate from eachother, this can result in a loss in accuracy and the relationship candegrade, also increasing the amount of noise. By keeping the amplitudeconsistent using the amplitude correction factor, this allows for betterdirection determination and better accuracy in the switching locations.By generating two lines at the desired phase shift and maintaining asclose to the original amplitude as possible, the virtual signals reduceerrors and/or noise in the signal processing.

The amplitude correction factor can be programmed into the IC at thetime of manufacture, based upon customer preferences given the knowntarget-sensor relationship based on the known phase separation, or thesensor can detect the phase separation after manufacture and calculatethe amplitude correction factor K during normal runtime operation of themagnetic field sensor. The amplitude correction factor is determinedbased upon an expected value of the phase difference between the atmeasured magnetic field signals as characterized at time of manufacture.The amplitude correction factor can be stored as a look-up table. Thecontroller of the magnetic field sensor (e.g., controller 180 in FIG.10C) can be configured to determine the phase difference between the twomeasured magnetic field signals and use the determined phase differenceto select the amplitude correction factor.

FIG. 21 is a flow diagram illustrating a method of generating one ormore virtual quadrature signals. At block 1210, the method starts bygenerating at least two measured magnetic field signals indicative of amagnetic field affected by an object. The at least two measured magneticfield signals have a phase difference with respect to each other. Thisphase difference may be known and/or provided by a customer ormanufacturer (which may be referred to herein as predetermined) or maybe unknown and determined by the magnetic field sensor (e.g., bycontroller 180) in accordance with the techniques of the presentdisclosure. The phase difference may, but need not be precisely90-degrees.

The method continues to block 1220 by processing the at least twomeasured magnetic field signals to generate at least a first virtualquadrature signal and at least a second virtual quadrature signal. Thefirst and second virtual quadrature signals have a predetermined phasedifference with respect to each other, which for example can be90-degrees to provide the quadrature virtual magnetic field signals.Processing the at least two measured magnetic field signals can include,at block 1222, averaging the first measured magnetic field signal andthe second measured magnetic field signal (see, e.g., Equation 40 above)to generate the first virtual quadrature signal. Processing the at leasttwo measured magnetic field signals can further include, at block 1224,determining the difference between the first measured magnetic fieldsignal and the second measured magnetic field signal (see, e.g.,Equation 41 above) to generate the second virtual quadrature signal.Processing the at least two measured magnetic field signals can furtherinclude (optionally) applying an amplitude correction factor to thesecond virtual quadrature signal, and the amplitude correction factor isbased upon the phase difference between the at least two measuredmagnetic field signals. Refer, for example, to Equation 41 herein thatutilizes the amplitude correction factor, K, in processing the twomeasured magnetic field signals. It will be appreciated that theamplitude correction factor processing is not always required and may beomitted in some implementations.

In accordance with the techniques described herein, at block 1230, thefirst virtual quadrature signal and the second virtual quadrature signalcan be processed according to a mathematical function (e.g., Equation39) that characterizes a relationship between the first and secondvirtual quadrature signals to generate at least one virtual magneticfield signal having a predetermined phase difference with respect to atleast one of the first and second virtual quadrature signals. As such,the first and second virtual quadrature signals can be further processedto achieve any number of virtual magnetic field signals using theseidealized virtual quadrature signals as a starting point, for exampleusing the techniques from FIGS. 10-13.

In some instances, it may be desirable to generate virtual signalshaving any arbitrary phase difference with respect to each other (e.g.,rather than having the quadrature phase difference that results from theprocess of FIG. 21 for example) and not being dependent on starting withmeasured magnetic field signals that are in perfect quadrature in orderimprove the accuracy of processing the virtual signals. It is desirableto have high accuracy and equidistant output signal pulse or transitionspacing when performing, for example, wheel displacement calculations,or the error can be very large (refer, for example, to FIG. 17 showing alarge error in wheel displacement).

FIG. 22 is a diagram of an example virtual signal generator 182″ forgenerating virtual arbitrary signals, according to the disclosure. Thevirtual signal generator 182″ can be the same as, or similar to, thevirtual signal generator 182′ shown in FIG. 18, the virtual signalgenerator 182 shown in FIG. 10C, or the virtual signal generator 142shown in FIG. 5B and can be configured to generate each of the virtualmagnetic field signals (e.g., FIGS. 10-13), the virtual quadraturesignals (e.g., FIGS. 18-21) and the virtual arbitrary signals (e.g.,FIGS. 22-23). The virtual signal generator 182″ uses a coefficient unit1310 to generate virtual arbitrary magnetic field signals, also referredto herein more generally as virtual arbitrary signals. Any of thecontrollers 182, 182′, or 182″ can be used to generate each of thevirtual signals shown and/or described herein.

The coefficient unit 1310 includes a coefficient generating unit 1312for generating the coefficient when the coefficient is generated on-chip(i.e., within the controller of the magnetic field sensor) and acoefficient storing unit 1314 for storing the coefficient when thecoefficients are generated both on-chip and off-chip (i.e., at time ofmanufacture). The techniques herein implement both on-chip and off-chipprocessing of the coefficients for the mathematical functions tocalculate the virtual arbitrary signals. Meaning, the on-chip processingdetermines the phase difference and the coefficients on the magneticfield sensor chip (i.e., by controller 182, 182′, or 182″) and theoff-chip processing determines the coefficients during the manufactureof the sensor and these values are stored and used later by thecontroller during operation of the sensor. It will be appreciated thatwhen the phase difference between the two measured magnetic fieldsignals is known, the coefficients can be calculated off-chip using thisknown phase difference (based on a shape of the object and an airgapbetween the magnetic field sensor and the object), and when the phasedifference is not known, it can be determined on-chip and used todetermine the coefficients on-chip as well. Because the air gap betweenthe sensor and the target object is known, this provides thecircumference of the target object that is presented to the magneticfield sensor, and the sensing elements have a known specific spacing, sothe resulting phase shift can be calculated. Thus, by measuring the twochannels, the phase difference can be calculated on-the-fly (on-chip) bythe coefficient generation unit 1312.

The virtual signal generator 182″ is responsive to the at least twomeasured magnetic field signals generated by the magnetic field sensingelements (e.g., 20 a, 20 b, 20 c of FIG. 10, 20 a′, 20 b′ of FIG. 10A,118 a, 118 b, 120 of FIG. 10B, 170 a, 170 b, 170 c, of FIG. 10C) and isconfigured to generate at least one virtual magnetic field signal havinga second predetermined phase difference with respect to at least one ofthe measured magnetic field signals. The second predetermined phasedifference may be any arbitrary value. In some embodiments, the secondpredetermined phase difference depends upon the number of equidistantoutput pulses desired per cycle of the magnetic field signal. Forexample, Table 3 shows various embodiments where more than a singlevirtual channel is generated for a particular application, as well asthe corresponding (Pt increment (the intended phase increment betweeneach virtual channel).

TABLE 3 Desired Number of Number Equidistant of Virtual Output ChannelsCommutations Required φ_(i) Increment (°) φ_(i) Values (°) 4 1 90 −90 62 60 −60, −120 8 3 45 −45, −90, −135 10 4 36 −36, −72, −108, −144 12 530 −30, −60, −90, −120, −150

In general, each virtual channel allows for at least two additionaloutput commutations in single threshold applications (e.g., the risingand falling portions of the sinusoidal magnetic field signal). Thenumber of output commutations are shown as each output pulse (forexample, refer to FIG. 14 showing output pulses 520 a-520 h, eachequidistant in spacing). Accordingly, the number of output commutations(N_(OC)) is dependent upon the number of virtual channels (N_(VC)), asshown in Equation 42 below:

N _(OC)=2×(N _(VC)+1)  Equation 42

Note that the virtual channel provides two output communications in asingle threshold implementation (2×N_(VC)), and the reference channel(the real channel) will provide two output commutations as well, thusproviding 2*N_(VC)+2 total number of channels, simplified into Equation42 above. Note that there is a ratio between the number of virtualchannels and the number of output commutations of two times the numberof virtual channels plus one. Accordingly, when there are, for example,10 equidistant output commutations desired, at least four virtualchannels are required, and the increment for the phase is thus 36degrees. More specifically, when taking 360, the total number ofdegrees, and dividing by 10, the number of output commutations, then onearrives at 36 which is phase increment (ϕi per channel). Thus, eachvirtual channel must be separated by 36 degrees, and the resulting phasedifference values for each virtual signal are 36-degrees, 72-degrees,108-degrees, and 144-degrees. As shown in Table 3, the secondpredetermined phase difference of the virtual arbitrary signal generatedfrom the first and second measured magnetic field signals can have aphase shift of (a) 90-degrees, or (b) 60-degrees and 120-degrees, or (c)45-degrees, 90-degrees, and 135-degrees, or (d) 36-degrees, 72-degrees,108-degrees, and 144-degrees, or (e) 30-degrees, 60-degrees, 90-degrees,120-degrees, and 150-degrees. Other phase differences are possible aswill be appreciated in light of the present disclosure.

FIG. 23 is a flow diagram illustrating a method of generating one ormore virtual arbitrary signals, according to the disclosure. At block1410, the method starts by generating at least two measured magneticfield signals indicative of a magnetic field affected by an object. Theat least two measured magnetic field signals have a phase differencewith respect to each other, which phase difference may, but need not be90-degrees.

At block 1420, the measured magnetic field signals are processed togenerate at least one virtual signal having a second phase shift withrespect to at least one of the measured magnetic field signals. Thesecond phase shift is predetermined to provide the virtual signal withan arbitrary phase shift relative to at least one of the measuredmagnetic field signals in order to achieve a desired number of outputcommutations (e.g., equidistant output pulses). At block 1422, a firstcoefficient is determined corresponding to a first channel, the firstcoefficient is based on the first phase difference and the second phasedifference. At block 1424, a second coefficient is determinedcorresponding to a second channel, the second coefficient based on thefirst phase difference and the second phase difference. The first andsecond coefficient are then used at block 1430 to generate at least onevirtual magnetic field signal using the first coefficient and the secondcoefficient. The measured magnetic field signals are processed accordingto the following mathematical formula(es) to achieve the desired numberof arbitrary virtual channel(s) by generating the first coefficient andthe second coefficient.

To generate one or more arbitrarily shifted phase signal virtualsignals, the two measured magnetic field signals are processed (e.g., bycontroller 182, 182′, or 182″). The two sinusoidal-shaped signals, orgenerally measured magnetic field signals, are denoted “L” and “R” inthe following equations 43 and 44, and are arbitrarily shifted withrespect to each other.

L=A _(L)·cos(2πƒt)+O _(L)  Equation 43

R=A _(R)·cos(2πƒt+ϕP)+O _(R)  Equation 44

The phase shift between L and R can be arbitrary (as long as it isnon-zero) and is denoted as ϕP in the equations herein. In Equation 43and Equation 44, A_(L) and O_(L) are the amplitude and offset of L,respectively, and likewise A_(R) and O_(R) are the amplitude and offsetof R, respectively. An arbitrarily phase shifted virtual channel, V_(i),could then be defined as in Equation 45:

V _(i) =A _(i)·cos(2πƒt+ϕi)+O _(i)  Equation 45

where A_(i), ϕ_(i), and O_(i) are the desired amplitude of the virtualsignal, the desired phase shift relative to L, and the resultant offset,respectively. This virtual signal can be derived from L and R usingEquation 46:

V _(i) =a _(i) ·L+b _(i) ·R  Equation 46

where a_(i) and b_(i) are two parameters which may be (referred toherein as “the first coefficient” and “the second coefficient”respectively), and depend upon ϕP, A_(i), and ϕi. The first coefficienta_(i) and the second coefficient b_(i) and can be calculated usingEquation 47 and Equation 48:

$\begin{matrix}{a_{i} = {\left( \frac{A_{i}}{A_{L}} \right)\left\lbrack {{\cos \left( \varphi_{i} \right)} - \left( \frac{\sin \left( \varphi_{i} \right)}{\tan \left( \varphi_{P} \right)} \right)} \right\rbrack}} & {{Equation}\mspace{14mu} 47} \\{b_{i} = {\left( \frac{A_{i}}{A_{R}} \right)\left( \frac{\sin \left( \varphi_{i} \right)}{\sin \left( \varphi_{P} \right)} \right)}} & {{Equation}\mspace{14mu} 48}\end{matrix}$

In the cases of L and R normalization or when the amplitudes of L, R,and the desired amplitude of V_(i) are approximately equal, theseequations simplify to Equation 49 and Equation 50:

$\begin{matrix}{a_{i} = {{\cos \left( \varphi_{i} \right)} - \left( \frac{\sin \left( \varphi_{i} \right)}{\tan \left( \varphi_{P} \right)} \right)}} & {{Equation}\mspace{14mu} 49} \\{b_{i} = \frac{\sin \left( \varphi_{i} \right)}{\sin \left( \varphi_{P} \right)}} & {{Equation}\mspace{14mu} 50}\end{matrix}$

Refer, for example, to FIG. 10 showing two measured magnetic fieldsignals and two virtual signals, as well as equidistant output spacing.By calculating and solving for these coefficients, any number ofarbitrary virtual signals can be generated in accordance with thepresent disclosure. Thus, the virtual channel V_(i) can be derived fromEquation 46 once the coefficients are solved for.

It will be appreciated that the measured magnetic field signals may ormay not be used in the further processing, for example determining wheeldisplacement or other positional information. For example, both themeasured magnetic field signals and the generated virtual signals may beused to determine position information, or position information may bedetermined using only the generated virtual signals. It will beappreciated that in applications in which the required number of virtualsignals is an odd number, the measured channel output signals may not beused for target detection. In other words, if the number of virtualsignals is such that their even phase separation within each 360° periodwould result in uneven phase separation with respect to the measuredmagnetic field signals, then only the virtual channel output signals maybe used to control the target. For example, if the user programmedresolution and target are such as to require that five virtual magneticfield signals be generated at relative phases of 60° and 120°, then themeasured magnetic field signals at approximately 0° and 90° can beignored for target control purposes.

It will further be appreciated that although only a single threshold isused for the detectors (e.g., at a 50% midpoint between positive peakand negative peak values) that is applied to the magnetic fieldsignal(s), multiple thresholds per signal may be implemented and may beselected to yield communication equidistance. Additional thresholdsapplied to the magnetic field signal(s) can improve accuracy of themagnetic field sensor.

All references cited herein are hereby incorporated herein by referencein their entirety. Having described preferred embodiments, it will nowbecome apparent to one of ordinary skill in the art that otherembodiments incorporating their concepts may be used. It is felttherefore that these embodiments should not be limited to disclosedembodiments, but rather should be limited only by the spirit and scopeof the appended claims.

What is claimed is:
 1. A method comprising: generating first and secondmagnetic field signals having a predetermined phase difference withrespect to each other, the first and second magnetic field signalsindicative of a magnetic field affected by an object; generating anangle signal from the first and second magnetic field signals, the anglesignal indicative of an angle of the magnetic field; and comparing theangle signal to a at least one angle signal threshold to generate a atleast one output transition.
 2. The method of claim 1, whereingenerating the second magnetic field signal comprises generating avirtual magnetic field signal from the second magnetic field signal,wherein the virtual magnetic field signal has a second predeterminedphase difference with respect to the first magnetic field signal, andwherein the angle signal is generated from the first magnetic fieldsignal and the virtual magnetic field signal.
 3. The method of claim 1,wherein generating the first and second magnetic field signals comprisesgenerating first and second virtual magnetic field signals fromrespective first and second measured magnetic field signals, the firstand second virtual magnetic field signals having a second predeterminedphase difference with respect to each other.
 4. The method of claim 3,wherein the virtual magnetic field signals are generated according to amathematical function that characterizes a relationship between thesecond predetermined phase difference and at least one of the twomeasured magnetic field signals.
 5. The method of claim 1, wherein thepredetermined phase difference is 90 degrees.
 6. The method of claim 1,wherein a direction of rotation of the object is determined based on apolarity of a slope of the angle signal.
 7. The method of claim 1,further comprising comparing the first magnetic field signal to aposcomp threshold to generate a first square wave signal, and comparingthe second magnetic field signal to the poscomp threshold to generate asecond square wave signal, and wherein a direction of rotation of theobject is determined by determining whether the first square wave signalleads or lags the second square wave signal.
 8. The method of claim 7,wherein the poscomp threshold is predetermined or is based on anamplitude of the first magnetic field signal and the second magneticfield signal.
 9. The method of claim 1, further comprising: comparingthe angle signal to a plurality of angle signal thresholds to generate acorresponding plurality of output transitions, each output transitionindicative of the angle signal crossing the corresponding angle signalthreshold.
 10. The method of claim 1, wherein the plurality of anglesignal thresholds comprises at least four thresholds.
 11. The method ofclaim 1, wherein a number of angle signal thresholds of the plurality ofangle signal thresholds is dependent upon a desired number of outputtransitions per pole-pair of the angle signal.
 12. The method of claim11, wherein the angle signal thresholds are generated according to theequations:${k = {\frac{N_{OC}}{2} - 1}},{N_{OC} = 2},4,6,{\ldots \mspace{14mu};{and}}$${{T\left( N_{OC} \right)} = {\left( \frac{\pi}{N_{OC}} \right) \cdot \left\{ {\tau_{0}\mspace{14mu} \ldots \mspace{14mu} \tau_{k}} \right\}}},{{\tau_{i} = {{2 \cdot i} - k}};}$Where τ is a threshold number, k is the total number of angle signalthresholds, N_(OC) is a desired number of output transitions, and T is avalue of the threshold number for each threshold.
 13. The method ofclaim 1, wherein the angle signal is calculated according to amathematical function that integrates a time derivative of the first andsecond magnetic field signals.
 14. The method of claim 13, wherein themathematical function comprises:${y = {{\arctan \left( {f(t)} \right)} = {\int{\frac{f^{\prime}(t)}{1 + {f^{2}(t)}}{dt}}}}},$where ƒ(t) is a function that is based on a ratio of the first andsecond magnetic field signals.
 15. A magnetic field sensor comprising: aplurality of magnetic field sensing elements configured to generate atleast two measured magnetic field signals indicative of a magnetic fieldaffected by an object and having a predetermined phase difference withrespect to each other; and a controller responsive to the at least twomeasured magnetic field signals and configured to generate an anglesignal and to compare the angle signal to at least one angle signalthreshold and to generate at least one output transition.
 16. Themagnetic field sensor of claim 15, wherein the phase difference ispredetermined.
 17. The magnetic field sensor of claim 16, wherein thephase difference is 90-degrees.
 18. The magnetic field sensor of claim15, wherein the controller is further configured to determine adirection of rotation of the object is based on a polarity of a slope ofthe angle signal.
 19. The magnetic field sensor of claim 15, wherein thecontroller is further configured to compare the first magnetic fieldsignal to a poscomp threshold to generate a first square wave signal,and compare the second magnetic field signal to the poscomp threshold togenerate a second square wave signal, and to determine a direction ofrotation of the object is by determining whether the first square wavesignal leads or lags the second square wave signal.
 20. The magneticfield sensor of claim 15, wherein the controller is configured tocompare the angle signal to a plurality of angle signal thresholds andto generate a plurality of output transitions, each output transitionindicative of the angle signal crossing the corresponding angle signalthreshold.
 21. The magnetic field sensor of claim 20, wherein theplurality of thresholds comprises at least four thresholds.
 22. Themagnetic field sensor of claim 20, wherein a number of angle signalthresholds of the plurality of angle signal thresholds is dependent upona desired number of output transitions per pole-pair of the anglesignal.
 23. The magnetic field sensor of claim 22, wherein the anglesignal thresholds are generated according to the equations:${k = {\frac{N_{OC}}{2} - 1}},{N_{OC} = 2},4,6,{\ldots \mspace{14mu};{and}}$${{T\left( N_{OC} \right)} = {\left( \frac{\pi}{N_{OC}} \right) \cdot \left\{ {\tau_{0}\mspace{14mu} \ldots \mspace{14mu} \tau_{k}} \right\}}},{{\tau_{i} = {{2 \cdot i} - k}};}$where τ is a threshold number, k is a total number of angle signalthresholds, N_(OC) is a desired number of output transitions, and T is avalue of the threshold number for each threshold number.
 24. Themagnetic field sensor of claim 15, wherein the angle signal iscalculated according to a mathematical function that integrates a timederivative of the first and second magnetic field signals.
 25. Themethod of claim 24, wherein the mathematical function comprises:${y = {{\arctan \left( {f(t)} \right)} = {\int{\frac{f^{\prime}(t)}{1 + {f^{2}(t)}}{dt}}}}},$where ƒ(t) is a function that is based on a ratio of the first andsecond magnetic field signals.
 26. The method of claim 15, wherein theoutput transitions are equidistant with respect to each other.
 27. Themethod of claim 15, wherein the output transitions are equidistant eachperiod-on-period of the angle signal.
 28. The method of claim 15,wherein the arctangent of the first and second magnetic field signals isdetermined without the sample time of the angle signal.
 29. The magneticfield sensor of claim 15, wherein the plurality of magnetic fieldsensing elements comprises one or more Hall effect elements and/ormagnetoresistance elements.
 30. A magnetic field sensor comprising:means for generating first and second magnetic field signals having apredetermined phase difference with respect to each other, the first andsecond magnetic field signals indicative of a magnetic field affected byan object; means for generating an angle signal from the first andsecond magnetic field signals, the angle signal indicative of an angleof the magnetic field; and means for comparing the angle signal to atleast one angle signal threshold to generate at least one outputtransition.
 31. The magnetic field sensor of claim 30, wherein the meansfor generating the first and second magnetic field signals comprisesmeans for generating first and second virtual magnetic field signalsfrom respective first and second measured magnetic field signals.